Вынесите общий множитель за скобки 18*a^5-60*a^2*b+50*a*b^3 (18 умножить на a в степени 5 минус 60 умножить на a в квадрате умножить на b плюс 50 умножить на a умножить на b в кубе) контрольная работа по алгебре 7 класс [Есть ответ!]
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Общий множитель 18*a^5-60*a^2*b+50*a*b^3

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Примеры

Решение

Комбинаторика [src]
    /   4       3         \
2*a*\9*a  + 25*b  - 30*a*b/
$$2 a \left(9 a^{4} - 30 a b + 25 b^{3}\right)$$
Разложение на множители [src]
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  |    ||                                                                                                                                  /                                  /   3 /   2       2/3 3 ____   /   3 /   2                                                                                                                                           3    || |    ||                                                                                                                                /                                  /   3 /   2       2/3 3 ____   /   3 /   2                                                                                                                                           3    || |    ||                                                                                                                                 /                                  /   3 /   2       2/3 3 ____   /   3 /   2                                                                                                                                          3    || |    ||                                                                                                                                /                                  /   3 /   2       2/3 3 ____   /   3 /   2                                                                                                                                           3    ||
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  |    ||                                                                                                                              /           /      /          9        4        2                            3                                                                                                                                                   || |    ||               /           /      /          9        4        2                            3                                                                                                                                                                                                                                                                || |    ||                                                                                                                            /           /      /          9        4        2                            3                                                                                                                                                   || |    ||                                                                                                                            /           /      /          9        4        2                            3                                                                                                                                                   ||
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  |    ||              ______________________________________________________________________________________________               /          \/     \/       19683      1296       36              ____________________________________                 ______________________________________________________________________________________________                || |    ||            /          \/     \/       19683      1296       36              ____________________________________                 ______________________________________________________________________________________________                ______________________________________________________________________________________________               || |    ||            ______________________________________________________________________________________________               /          \/     \/       19683      1296       36              ____________________________________                 ______________________________________________________________________________________________                || |    ||            ______________________________________________________________________________________________               /          \/     \/       19683      1296       36              ____________________________________                 ______________________________________________________________________________________________                ||
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  |    ||            /         /      _____________________                                                                       /                                                                /      /          9        4        2                /         /      _____________________                                                                          || |    ||          /                                                                /      /          9        4        2                /         /      _____________________                                                                        /         /      _____________________                                                                         || |    ||          /         /      _____________________                                                                       /                                                                /      /          9        4        2                /         /      _____________________                                                                          || |    ||          /         /      _____________________                                                                       /                                                                /      /          9        4        2                /         /      _____________________                                                                          ||
  |    ||           /         /      /          9        4        2                            3                                 /                                                                /      /    15625*b    625*b     25*b                /         /      /          9        4        2                            3                                     || |    ||         /                                                                /      /    15625*b    625*b     25*b                /         /      /          9        4        2                            3                                  /         /      /          9        4        2                            3                                    || |    ||         /         /      /          9        4        2                            3                                 /                                                                /      /    15625*b    625*b     25*b                /         /      /          9        4        2                            3                                     || |    ||         /         /      /          9        4        2                            3                                 /                                                                /      /    15625*b    625*b     25*b                /         /      /          9        4        2                            3                                     ||
  |    ||          /         /      /    15625*b    625*b     25*b                         50*b                                 /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                      || |    ||        /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                  /         /      /    15625*b    625*b     25*b                         50*b                                     || |    ||        /         /      /    15625*b    625*b     25*b                         50*b                                 /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                      || |    ||        /         /      /    15625*b    625*b     25*b                         50*b                                 /                                                           27*3 /      /   - -------- + ------  + -----              /         /      /    15625*b    625*b     25*b                         50*b                                      ||
  |    ||         /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------           /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                 || |    ||       /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------            /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                || |    ||       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------           /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                 || |    ||       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------           /                                                               \/     \/       19683      1296       36     3*       /     2*3 /      /   - -------- + ------  + -----  + ---------------------------------------------                 ||
  |    ||        /        \/     \/       19683      1296       36              ____________________________________          /                                                                                                                     /        \/     \/       19683      1296       36              ____________________________________                 || |    ||      /                                                                                                                     /        \/     \/       19683      1296       36              ____________________________________           /        \/     \/       19683      1296       36              ____________________________________                || |    ||      /        \/     \/       19683      1296       36              ____________________________________          /                                                                                                                     /        \/     \/       19683      1296       36              ____________________________________                 || |    ||      /        \/     \/       19683      1296       36              ____________________________________          /                                                                                                                     /        \/     \/       19683      1296       36              ____________________________________                 ||
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  |    ||     /                                                              /      /    15625*b    625*b     25*b         /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b                   || |    ||   /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b          /                                                              /      /    15625*b    625*b     25*b                  || |    ||   /                                                              /      /    15625*b    625*b     25*b         /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b                   || |    ||   /                                                              /      /    15625*b    625*b     25*b         /                                                                                                                     /                                                              /      /    15625*b    625*b     25*b                   ||
  |    ||    /                                                         27*3 /      /   - -------- + ------  + -----       /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----                  || |    ||  /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----        /                                                         27*3 /      /   - -------- + ------  + -----                 || |    ||  /                                                         27*3 /      /   - -------- + ------  + -----       /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----                  || |    ||  /                                                         27*3 /      /   - -------- + ------  + -----       /                                                                                                                     /                                                         27*3 /      /   - -------- + ------  + -----                  ||
  |    ||  \/                                                             \/     \/       19683      1296       36      \/                                                                                                                    \/                                                             \/     \/       19683      1296       36                   || |    ||\/                                                                                                                    \/                                                             \/     \/       19683      1296       36       \/                                                             \/     \/       19683      1296       36                  || |    ||\/                                                             \/     \/       19683      1296       36      \/                                                                                                                    \/                                                             \/     \/       19683      1296       36                   || |    ||\/                                                             \/     \/       19683      1296       36      \/                                                                                                                    \/                                                             \/     \/       19683      1296       36                   ||
  |    ||- ---------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------    otherwise  || |    ||--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------    otherwise  || |    ||---------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------    otherwise  || |    ||---------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------    otherwise  ||
  |    ||                                                      2                                                                                                                                                                        2                                                                                                                               || |    ||                                                                                                                2                                                                                                                                                                       2                                                                    || |    ||                                                    2                                                                                                                                                                        2                                                                                                                               || |    ||                                                    2                                                                                                                                                                        2                                                                                                                               ||
  \    \\                                                                                                                                                                                                                                                                                                                                                               // \    \\                                                                                                                                                                                                                                                                                                                                                             // \    \\                                                                                                                                                                                                                                                                                                                                                             // \    \\                                                                                                                                                                                                                                                                                                                                                             //
$$a \left(a - \begin{cases} - \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} - \frac{\sqrt{- \frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\- \frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} - \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} - \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right) \left(a - \begin{cases} - \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} + \frac{\sqrt{- \frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\- \frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} + \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} - \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right) \left(a - \begin{cases} \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} - \frac{\sqrt{\frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\\frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} - \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right) \left(a - \begin{cases} \frac{\sqrt[3]{10} \cdot 3^{\frac{2}{3}} \sqrt{- \sqrt[3]{- b^{2}}}}{6} + \frac{\sqrt{\frac{2 \cdot 10^{\frac{2}{3}} \sqrt[3]{3} b}{3 \sqrt{- \sqrt[3]{- b^{2}}}} + \frac{\sqrt[3]{12} \cdot 5^{\frac{2}{3}} \sqrt[3]{- b^{2}}}{3}}}{2} & \text{for}\: \frac{25 b^{3}}{9} = 0 \\\frac{\sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} + \frac{\sqrt{- \frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + \frac{20 b}{3 \sqrt{\frac{50 b^{3}}{27 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}} + 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}} - 2 \sqrt[3]{\frac{25 b^{2}}{36} + \sqrt{- \frac{15625 b^{9}}{19683} + \frac{625 b^{4}}{1296}}}}}{2} & \text{otherwise} \end{cases}\right)$$
Объединение рациональных выражений [src]
    /    3       /           3\\
2*a*\25*b  + 3*a*\-10*b + 3*a //
$$2 a \left(3 a \left(3 a^{3} - 10 b\right) + 25 b^{3}\right)$$
Общее упрощение [src]
    /   4       3         \
2*a*\9*a  + 25*b  - 30*a*b/
$$2 a \left(9 a^{4} - 30 a b + 25 b^{3}\right)$$
Собрать выражение [src]
    5         2         3
18*a  - 60*b*a  + 50*a*b
$$18 a^{5} - 60 a^{2} b + 50 a b^{3}$$