Разложить многочлен на множители x^3+3*x^2*y-6*x*y^2-2^3

Объединение рациональных выражений

       /     2              \
-8 + x*\- 6*y  + x*(x + 3*y)/

$$x \left(x \left(x + 3 y\right) - 6 y^{2}\right) - 8$$

Комбинаторика

      3        2        2
-8 + x  - 6*x*y  + 3*y*x 

$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$

Разложение на множители

/               ___________________________________________________                                                             \ /               ___________________________________________________                                                                                             \ /               ___________________________________________________                                                                                             \
|              /            _____________________________                                                                       | |              /            _____________________________                                                                                                       | |              /            _____________________________                                                                                                       |
|             /            /                2                                                                                   | |             /            /                2                                                                                                                   | |             /            /                2                                                                                                                   |
|            /            /  /            3\           6                                                                        | |            /            /  /            3\           6            /          ___\                                                                             | |            /            /  /            3\           6            /          ___\                                                                             |
|           /           \/   \-216 + 216*y /  - 78732*y          3                                                              | |           /           \/   \-216 + 216*y /  - 78732*y          3  |  1   I*\/ 3 |                                                                             | |           /           \/   \-216 + 216*y /  - 78732*y          3  |  1   I*\/ 3 |                                                                             |
|        3 /     -108 + --------------------------------- + 108*y                                   2                           | |        3 /     -108 + --------------------------------- + 108*y  *|- - - -------|                                         2                                   | |        3 /     -108 + --------------------------------- + 108*y  *|- - + -------|                                         2                                   |
|        \/                             2                                                        9*y                            | |        \/                             2                           \  2      2   /                                      9*y                                    | |        \/                             2                           \  2      2   /                                      9*y                                    |
|x + y + ---------------------------------------------------------- + ----------------------------------------------------------|*|x + y + -------------------------------------------------------------------------- + --------------------------------------------------------------------------|*|x + y + -------------------------------------------------------------------------- + --------------------------------------------------------------------------|
|                                    3                                       ___________________________________________________| |                                            3                                                               ___________________________________________________| |                                            3                                                               ___________________________________________________|
|                                                                           /            _____________________________          | |                                                                                                           /            _____________________________          | |                                                                                                           /            _____________________________          |
|                                                                          /            /                2                      | |                                                                                                          /            /                2                      | |                                                                                                          /            /                2                      |
|                                                                         /            /  /            3\           6           | |                                                                                     /          ___\     /            /  /            3\           6           | |                                                                                     /          ___\     /            /  /            3\           6           |
|                                                                        /           \/   \-216 + 216*y /  - 78732*y          3 | |                                                                                     |  1   I*\/ 3 |    /           \/   \-216 + 216*y /  - 78732*y          3 | |                                                                                     |  1   I*\/ 3 |    /           \/   \-216 + 216*y /  - 78732*y          3 |
|                                                                     3 /     -108 + --------------------------------- + 108*y  | |                                                                                     |- - - -------|*3 /     -108 + --------------------------------- + 108*y  | |                                                                                     |- - + -------|*3 /     -108 + --------------------------------- + 108*y  |
\                                                                     \/                             2                          / \                                                                                     \  2      2   / \/                             2                          / \                                                                                     \  2      2   / \/                             2                          /

$$\left(x + \left(\frac{9 y^{2}}{\sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}} + y + \frac{\sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}}{3}\right)\right) \left(x + \left(\frac{9 y^{2}}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}} + y + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}}{3}\right)\right) \left(x + \left(\frac{9 y^{2}}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}} + y + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}}{3}\right)\right)$$