Вынесите общий множитель за скобки 4*c^4-6*x^2-c^2+8*c^3 (4 умножить на c в степени 4 минус 6 умножить на х в квадрате минус c в квадрате плюс 8 умножить на c в кубе) контрольная работа по алгебре 7 класс [Есть ответ!]
Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ Общий множитель за скобки/ 4*c^4-6*x^2-c^2+8*c^3

Общий множитель 4*c^4-6*x^2-c^2+8*c^3

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Разложение на множители [src]
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|    ||                                                                                                                                                                                                                                                                    /            /           2                                                                                                                                                                                                                                                                                || |    ||                                                                                                                                                                                                                                 /            /           2                                                                                                                                                                                                                                                                                                                   || |    ||                                                                                                                                                                                                                                                                    /            /           2                                                                                                                                                                                                                                                                                || |    ||                                                                                                                                                                                                                                                                    /            /           2                                                                                                                                                                                                                                                                                ||
|    ||                                                                                                                                                                                                                                                                   /   7        /   1     7*x                     5                                                                                                                                                                                                                                                           || |    ||                                                                                                                                                                                                                                /   7        /   1     7*x                     5                                                                                                                                                                                                                                                                                              || |    ||                                                                                                                                                                                                                                                                   /   7        /   1     7*x                     5                                                                                                                                                                                                                                                           || |    ||                                                                                                                                                                                                                                                                   /   7        /   1     7*x                     5                                                                                                                                                                                                                                                           ||
|    ||                                                                                                                                                                                                                                                                  /    - + 2*3 /   ---- + ----  + ----------------------------------                                                                                                                                                                                                                                          || |    ||                                                                                                                                                                                                                               /    - + 2*3 /   ---- + ----  + ----------------------------------                                                                                                                                                                                                                                                                             || |    ||                                                                                                                                                                                                                                                                  /    - + 2*3 /   ---- + ----  - ----------------------------------                                                                                                                                                                                                                                          || |    ||                                                                                                                                                                                                                                                                  /    - + 2*3 /   ---- + ----  - ----------------------------------                                                                                                                                                                                                                                          ||
|    ||                                                                                                                                                                                                                              __________________________         /     3     \/    6912    8              __________________________                                                                                                                                                                                                                                          || |    ||                                                                                                                                                                                                                              /     3     \/    6912    8              __________________________          __________________________                                                                                                                                                                                                                                         || |    ||                                                                                                                                                                                                                              __________________________         /     3     \/    6912    8              __________________________                                                                                                                                                                                                                                          || |    ||                                                                                                                                                                                                                              __________________________         /     3     \/    6912    8              __________________________                                                                                                                                                                                                                                          ||
|    ||                                                                                                                                                                                                                             /            _____________         /                                        /            _____________                                                                                                                                                                                                                                           || |    ||                                                                                                                                                                                                                             /                                        /            _____________          /            _____________                                                                                                                                                                                                                                          || |    ||                                                                                                                                                                                                                             /            _____________         /                                        /            _____________                                                                                                                                                                                                                                           || |    ||                                                                                                                                                                                                                             /            _____________         /                                        /            _____________                                                                                                                                                                                                                                           ||
|    ||                                                                                                                                                                                                                            /            /           2         /                                        /            /           2                                                                                                                                                                                                                                            || |    ||                                                                                                                                                                                                                            /                                        /            /           2          /            /           2                                                                                                                                                                                                                                           || |    ||                                                                                                                                                                                                                            /            /           2         /                                        /            /           2                                                                                                                                                                                                                                            || |    ||                                                                                                                                                                                                                            /            /           2         /                                        /            /           2                                                                                                                                                                                                                                            ||
|    ||                                                                                                                                                                                                                           /   7        /   1     7*x         /                                        /   7        /   1     7*x                                                                                                                                                                                                                                             || |    ||                                                                                                                                                                                                                           /                                        /   7        /   1     7*x          /   7        /   1     7*x                                                                                                                                                                                                                                            || |    ||                                                                                                                                                                                                                           /   7        /   1     7*x         /                                        /   7        /   1     7*x                                                                                                                                                                                                                                             || |    ||                                                                                                                                                                                                                           /   7        /   1     7*x         /                                        /   7        /   1     7*x                                                                                                                                                                                                                                             ||
|    ||                                                                                                                                                                                                                          /    - - 2*3 /   ---- + ----       /                                    2*  /    - - 2*3 /   ---- + ----                                                                                                                                                                                                                                       2    || |    ||                                                                                                                                                                                                                          /                                    2*  /    - - 2*3 /   ---- + ----        /    - - 2*3 /   ---- + ----                                                                                                                                                                                                                                      2    || |    ||                                                                                                                                                                                                                          /    - - 2*3 /   ---- + ----       /                                    2*  /    - - 2*3 /   ---- + ----                                                                                                                                                                                                                                       2    || |    ||                                                                                                                                                                                                                          /    - - 2*3 /   ---- + ----       /                                    2*  /    - - 2*3 /   ---- + ----                                                                                                                                                                                                                                       2    ||
|    ||                                                                                                                                                                                                                    1   \/     6     \/    6912    8       \/                                       \/     6     \/    6912    8                                                                                                                                                                                                                                 1    3*x     || |    ||                                                                                                                                                                                                                    1   \/                                       \/     6     \/    6912    8        \/     6     \/    6912    8                                                                                                                                                                                                                                1    3*x     || |    ||                                                                                                                                                                                                                    1   \/     6     \/    6912    8       \/                                       \/     6     \/    6912    8                                                                                                                                                                                                                                 1    3*x     || |    ||                                                                                                                                                                                                                    1   \/     6     \/    6912    8       \/                                       \/     6     \/    6912    8                                                                                                                                                                                                                                 1    3*x     ||
|    ||                                                                                                                                                                                                                  - - - -------------------------------- - --------------------------------------------------------------------------                                                                                                                                                                                                                     for - --- + ---- = 0|| |    ||                                                                                                                                                                                                                  - - + -------------------------------------------------------------------------- - --------------------------------                                                                                                                                                                                                                     for - --- + ---- = 0|| |    ||                                                                                                                                                                                                                  - - + -------------------------------- - --------------------------------------------------------------------------                                                                                                                                                                                                                     for - --- + ---- = 0|| |    ||                                                                                                                                                                                                                  - - + -------------------------------- + --------------------------------------------------------------------------                                                                                                                                                                                                                     for - --- + ---- = 0||
|    ||                                                                                                                                                                                                                    2                  2                                                       2                                                                                                                                                                                                                                                                192    2      || |    ||                                                                                                                                                                                                                    2                                       2                                                       2                                                                                                                                                                                                                                           192    2      || |    ||                                                                                                                                                                                                                    2                  2                                                       2                                                                                                                                                                                                                                                                192    2      || |    ||                                                                                                                                                                                                                    2                  2                                                       2                                                                                                                                                                                                                                                                192    2      ||
|    ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              || |    ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              || |    ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              || |    ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ||
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|    ||                                                                                                                                                                                                            /                /                   /              2                 3                                                                                                                                                                                                                                                                                           || |    ||                              /                /                   /              2                 3                                                                                                                                                                                                                                                                                                                                                                                                                                                                         || |    ||                                                                                                                                                                                                            /                /                   /              2                 3                                                                                                                                                                                                                                                                                           || |    ||                                                                                                                                                                                                            /                /                   /              2                 3                                                                                                                                                                                                                                                                                           ||
|    ||                                                                                                                                                                                                           /                /                   /  /          2\    /           2\                                                                                                                                                                                                                           /           2\                                                   || |    ||                             /                /                   /  /          2\    /           2\                                                                                                                                                                                                                           /           2\                                                                                                                                                                                                                                 || |    ||                                                                                                                                                                                                           /                /                   /  /          2\    /           2\                                                                                                                                                                                                                           /           2\                                                   || |    ||                                                                                                                                                                                                           /                /                   /  /          2\    /           2\                                                                                                                                                                                                                           /           2\                                                   ||
|    ||                                                                                                                                                                                                          /                /                   /   | 1     7*x |    |   1    3*x |                                                                                                                                                                                                                           |   1    3*x |                                                   || |    ||                            /                /                   /   | 1     7*x |    |   1    3*x |                                                                                                                                                                                                                           |   1    3*x |                                                                                                                                                                                                                                 || |    ||                                                                                                                                                                                                          /                /                   /   | 1     7*x |    |   1    3*x |                                                                                                                                                                                                                           |   1    3*x |                                                   || |    ||                                                                                                                                                                                                          /                /                   /   | 1     7*x |    |   1    3*x |                                                                                                                                                                                                                           |   1    3*x |                                                   ||
|    ||                                                                                                                                                                                                         /                /                   /    |---- + ----|    |- --- + ----|        2                                                                                                                                                                                                                2*|- --- + ----|                                                   || |    ||                           /                /                   /    |---- + ----|    |- --- + ----|        2                                                                                                                                                                                                                2*|- --- + ----|                                                                                                                                                                                                                                 || |    ||                                                                                                                                                                                                         /                /                   /    |---- + ----|    |- --- + ----|        2                                                                                                                                                                                                                2*|- --- + ----|                                                   || |    ||                                                                                                                                                                                                         /                /                   /    |---- + ----|    |- --- + ----|        2                                                                                                                                                                                                                2*|- --- + ----|                                                   ||
|c - |<                                                                                                                                                                                                        /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                           5                                                                                                                       \  192    2  /                                                   ||*|c - |<                          /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                           5                                                                                                                       \  192    2  /                                                                                                                                                                                                                                 ||*|c - |<                                                                                                                                                                                                        /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                           5                                                                                                                       \  192    2  /                                                   ||*|c - |<                                                                                                                                                                                                        /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                           5                                                                                                                       \  192    2  /                                                   ||
|    ||                                                                                                                                                                                                       /        - - 2*3 /       - ----- +   /      -------------- + ---------------  - ----  + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------                       || |    ||                         /        - - 2*3 /       - ----- +   /      -------------- + ---------------  - ----  + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------                                                                                                                                                                                                     || |    ||                                                                                                                                                                                                       /        - - 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------                       || |    ||                                                                                                                                                                                                       /        - - 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------                       ||
|    ||                        _________________________________________________________________________________________________________________________________________________________                     /         3     \/          13824   \/             4                 27           16                         _________________________________________________________________________________________________________________________________________________________              _____________________________________________________________                       || |    ||                        /         3     \/          13824   \/             4                 27           16                         _________________________________________________________________________________________________________________________________________________________              _____________________________________________________________                      _________________________________________________________________________________________________________________________________________________________                      || |    ||                        _________________________________________________________________________________________________________________________________________________________                     /         3     \/          13824   \/             4                 27           16                         _________________________________________________________________________________________________________________________________________________________              _____________________________________________________________                       || |    ||                        _________________________________________________________________________________________________________________________________________________________                     /         3     \/          13824   \/             4                 27           16                         _________________________________________________________________________________________________________________________________________________________              _____________________________________________________________                       ||
|    ||                       /                _____________________________________________________________                                                                                                /                                                                                                            /                _____________________________________________________________                                                                                         /                   __________________________________                               || |    ||                       /                                                                                                            /                _____________________________________________________________                                                                                         /                   __________________________________                             /                _____________________________________________________________                                                                                                  || |    ||                       /                _____________________________________________________________                                                                                                /                                                                                                            /                _____________________________________________________________                                                                                         /                   __________________________________                               || |    ||                       /                _____________________________________________________________                                                                                                /                                                                                                            /                _____________________________________________________________                                                                                         /                   __________________________________                               ||
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|    ||                     /                /                   /              2                 3                                                                                                       /                                                                                                            /                /                   /              2                 3                                                                                                /                   /  /          2\    /           2\                                 || |    ||                     /                                                                                                            /                /                   /              2                 3                                                                                                /                   /  /          2\    /           2\                             /                /                   /              2                 3                                                                                                           || |    ||                     /                /                   /              2                 3                                                                                                       /                                                                                                            /                /                   /              2                 3                                                                                                /                   /  /          2\    /           2\                                 || |    ||                     /                /                   /              2                 3                                                                                                       /                                                                                                            /                /                   /              2                 3                                                                                                /                   /  /          2\    /           2\                                 ||
|    ||                    /                /                   /  /          2\    /           2\                                           /           2\                                              /                                                                                                            /                /                   /  /          2\    /           2\                                           /           2\                                       /                   /   | 1     7*x |    |   1    3*x |                                 || |    ||                    /                                                                                                            /                /                   /  /          2\    /           2\                                           /           2\                                       /                   /   | 1     7*x |    |   1    3*x |                            /                /                   /  /          2\    /           2\                                           /           2\                                                   || |    ||                    /                /                   /  /          2\    /           2\                                           /           2\                                              /                                                                                                            /                /                   /  /          2\    /           2\                                           /           2\                                       /                   /   | 1     7*x |    |   1    3*x |                                 || |    ||                    /                /                   /  /          2\    /           2\                                           /           2\                                              /                                                                                                            /                /                   /  /          2\    /           2\                                           /           2\                                       /                   /   | 1     7*x |    |   1    3*x |                                 ||
|    ||                   /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                             /                                                                                                            /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                      /                   /    |---- + ----|    |- --- + ----|        2                        || |    ||                   /                                                                                                            /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                      /                   /    |---- + ----|    |- --- + ----|        2                  /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                                   || |    ||                   /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                             /                                                                                                            /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                      /                   /    |---- + ----|    |- --- + ----|        2                        || |    ||                   /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                             /                                                                                                            /                /                   /   | 1     7*x |    |   1    3*x |                                           |   1    3*x |                                      /                   /    |---- + ----|    |- --- + ----|        2                        ||
|    ||                  /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                            /                                                                                                            /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                     /          1        /     \6912    8  /    \  192    2  /     7*x                         || |    ||                  /                                                                                                            /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                     /          1        /     \6912    8  /    \  192    2  /     7*x                  /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                                   || |    ||                  /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                            /                                                                                                            /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                     /          1        /     \6912    8  /    \  192    2  /     7*x                         || |    ||                  /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                            /                                                                                                            /                /                   /    |---- + ----|    |- --- + ----|        2                                2*|- --- + ----|                                     /          1        /     \6912    8  /    \  192    2  /     7*x                         ||
|    ||                 /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                           /                                                                                                            /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                3*3 /       - ----- +   /      -------------- + ---------------  - ----                        || |    ||                 /                                                                                                            /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                3*3 /       - ----- +   /      -------------- + ---------------  - ----                /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                                   || |    ||                 /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                           /                                                                                                            /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                3*3 /       - ----- +   /      -------------- + ---------------  - ----                        || |    ||                 /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                           /                                                                                                            /       7        /          1        /     \6912    8  /    \  192    2  /     7*x                                   \  192    2  /                                3*3 /       - ----- +   /      -------------- + ---------------  - ----                        ||
|    ||                /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------              /                                                                                                2*          /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------      \/          13824   \/             4                 27           16                         || |    ||                /                                                                                                2*          /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------      \/          13824   \/             4                 27           16                /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------                       || |    ||                /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------              /                                                                                                2*          /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------      \/          13824   \/             4                 27           16                         || |    ||                /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------              /                                                                                                2*          /        - + 2*3 /       - ----- +   /      -------------- + ---------------  - ----  - ------------------------------------------------------------------------      \/          13824   \/             4                 27           16                         ||
|    ||               /         6     \/          13824   \/             4                 27           16                _____________________________________________________________             /                                                                                                            /         6     \/          13824   \/             4                 27           16                _____________________________________________________________                                                                                                   || |    ||               /                                                                                                            /         6     \/          13824   \/             4                 27           16                _____________________________________________________________                                                                                         /         6     \/          13824   \/             4                 27           16                _____________________________________________________________                       || |    ||               /         6     \/          13824   \/             4                 27           16                _____________________________________________________________             /                                                                                                            /         6     \/          13824   \/             4                 27           16                _____________________________________________________________                                                                                                   || |    ||               /         6     \/          13824   \/             4                 27           16                _____________________________________________________________             /                                                                                                            /         6     \/          13824   \/             4                 27           16                _____________________________________________________________                                                                                                   ||
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|    ||             /                                                                                                   /                   /              2                 3                    /                                                                                                            /                                                                                                   /                   /              2                 3                                                                                                            || |    ||             /                                                                                                            /                                                                                                   /                   /              2                 3                                                                                                /                                                                                                   /                   /              2                 3                                || |    ||             /                                                                                                   /                   /              2                 3                    /                                                                                                            /                                                                                                   /                   /              2                 3                                                                                                            || |    ||             /                                                                                                   /                   /              2                 3                    /                                                                                                            /                                                                                                   /                   /              2                 3                                                                                                            ||
|    ||            /                                                                                                   /                   /  /          2\    /           2\                    /                                                                                                            /                                                                                                   /                   /  /          2\    /           2\                                                                                                             || |    ||            /                                                                                                            /                                                                                                   /                   /  /          2\    /           2\                                                                                                /                                                                                                   /                   /  /          2\    /           2\                                 || |    ||            /                                                                                                   /                   /  /          2\    /           2\                    /                                                                                                            /                                                                                                   /                   /  /          2\    /           2\                                                                                                             || |    ||            /                                                                                                   /                   /  /          2\    /           2\                    /                                                                                                            /                                                                                                   /                   /  /          2\    /           2\                                                                                                             ||
|    ||           /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                   /                                                                                                            /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                                                                                                             || |    ||           /                                                                                                            /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                                                                                               /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                                 || |    ||           /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                   /                                                                                                            /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                                                                                                             || |    ||           /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                   /                                                                                                            /                                                                                                   /                   /   | 1     7*x |    |   1    3*x |                                                                                                             ||
|    ||          /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2         /                                                                                                            /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2                                                                                                    || |    ||          /                                                                                                            /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2                                                                                     /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2                        || |    ||          /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2         /                                                                                                            /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2                                                                                                    || |    ||          /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2         /                                                                                                            /                                                                                                   /                   /    |---- + ----|    |- --- + ----|        2                                                                                                    ||
|    ||         /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x         /                                                                                                            /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                                     || |    ||         /                                                                                                            /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                     /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x                         || |    ||         /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x         /                                                                                                            /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                                     || |    ||         /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x         /                                                                                                            /                                                                                                   /          1        /     \6912    8  /    \  192    2  /     7*x                                                                                                     ||
|    ||        /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----       /                                                                                                            /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----                                                                                                    || |    ||        /                                                                                                            /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----                                                                                   /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----                        || |    ||        /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----       /                                                                                                            /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----                                                                                                    || |    ||        /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----       /                                                                                                            /                                                                                               3*3 /       - ----- +   /      -------------- + ---------------  - ----                                                                                                    ||
|    ||  1   \/                                                                                                  \/          13824   \/             4                 27           16      \/                                                                                                           \/                                                                                                  \/          13824   \/             4                 27           16                                                                                                     || |    ||  1   \/                                                                                                           \/                                                                                                  \/          13824   \/             4                 27           16                                                                                  \/                                                                                                  \/          13824   \/             4                 27           16                         || |    ||  1   \/                                                                                                  \/          13824   \/             4                 27           16      \/                                                                                                           \/                                                                                                  \/          13824   \/             4                 27           16                                                                                                     || |    ||  1   \/                                                                                                  \/          13824   \/             4                 27           16      \/                                                                                                           \/                                                                                                  \/          13824   \/             4                 27           16                                                                                                     ||
|    ||- - - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------       otherwise      || |    ||- - + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------       otherwise      || |    ||- - + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------       otherwise      || |    ||- - + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------       otherwise      ||
\    \\  2                                                                                        2                                                                                                                                                                                                                                                                         2                                                                                                                                                                                                        // \    \\  2                                                                                                                                                                                    2                                                                                                                                                                                                                                                                          2                                                                                                           // \    \\  2                                                                                        2                                                                                                                                                                                                                                                                         2                                                                                                                                                                                                        // \    \\  2                                                                                        2                                                                                                                                                                                                                                                                         2                                                                                                                                                                                                        //
$$\left(c - \begin{cases} - \frac{\sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}{2} - \frac{\sqrt{2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}} + \frac{7}{3} + \frac{5}{2 \sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}}}{2} - \frac{1}{2} & \text{for}\: \frac{3 x^{2}}{2} - \frac{1}{192} = 0 \\- \frac{\sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}{2} - \frac{\sqrt{\frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} - 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{3} + \frac{5}{2 \sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}}}{2} - \frac{1}{2} & \text{otherwise} \end{cases}\right) \left(c - \begin{cases} - \frac{\sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}{2} + \frac{\sqrt{2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}} + \frac{7}{3} + \frac{5}{2 \sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}}}{2} - \frac{1}{2} & \text{for}\: \frac{3 x^{2}}{2} - \frac{1}{192} = 0 \\- \frac{\sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}{2} + \frac{\sqrt{\frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} - 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{3} + \frac{5}{2 \sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}}}{2} - \frac{1}{2} & \text{otherwise} \end{cases}\right) \left(c - \begin{cases} \frac{\sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}{2} - \frac{\sqrt{2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}} + \frac{7}{3} - \frac{5}{2 \sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}}}{2} - \frac{1}{2} & \text{for}\: \frac{3 x^{2}}{2} - \frac{1}{192} = 0 \\\frac{\sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}{2} - \frac{\sqrt{\frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} - 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{3} - \frac{5}{2 \sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}}}{2} - \frac{1}{2} & \text{otherwise} \end{cases}\right) \left(c - \begin{cases} \frac{\sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}{2} + \frac{\sqrt{2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}} + \frac{7}{3} - \frac{5}{2 \sqrt{\frac{7}{6} - 2 \sqrt[3]{\frac{7 x^{2}}{8} + \frac{1}{6912}}}}}}{2} - \frac{1}{2} & \text{for}\: \frac{3 x^{2}}{2} - \frac{1}{192} = 0 \\\frac{\sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}{2} + \frac{\sqrt{\frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} - 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{3} - \frac{5}{2 \sqrt{- \frac{2 \left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)}{3 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}}} + 2 \sqrt[3]{- \frac{7 x^{2}}{16} + \sqrt{\frac{\left(\frac{7 x^{2}}{8} + \frac{1}{6912}\right)^{2}}{4} + \frac{\left(\frac{3 x^{2}}{2} - \frac{1}{192}\right)^{3}}{27}} - \frac{1}{13824}} + \frac{7}{6}}}}}{2} - \frac{1}{2} & \text{otherwise} \end{cases}\right)$$
Объединение рациональных выражений [src]
   2      2      4      3
- c  - 6*x  + 4*c  + 8*c
$$4 c^{4} + 8 c^{3} - c^{2} - 6 x^{2}$$
Комбинаторика [src]
   2      2      4      3
- c  - 6*x  + 4*c  + 8*c
$$4 c^{4} + 8 c^{3} - c^{2} - 6 x^{2}$$
Собрать выражение [src]
   2      2      4      3
- c  - 6*x  + 4*c  + 8*c
$$4 c^{4} + 8 c^{3} - c^{2} - 6 x^{2}$$
Общее упрощение [src]
   2      2      4      3
- c  - 6*x  + 4*c  + 8*c
$$4 c^{4} + 8 c^{3} - c^{2} - 6 x^{2}$$