Разложить многочлен на множители a^3+a+a*b^2+a^2*b-b-b^3

Комбинаторика

     3        3      2      2
a + a  - b - b  + a*b  + b*a 

$$a^{3} + a^{2} b + a b^{2} + a - b^{3} - b$$

Объединение рациональных выражений

      3     /     2    2      \
-b - b  + a*\1 + a  + b  + a*b/

$$a \left(a^{2} + a b + b^{2} + 1\right) - b^{3} - b$$

Разложение на множители

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|              /     __________________________________________________                                                                                                                                 | |              /     __________________________________________________                                                                                                                                                                 | |              /     __________________________________________________                                                                                                                                                                 |
|             /     /                               2                3                                                                                                                                  | |             /     /                               2                3                                                                                                                                                                  | |             /     /                               2                3                                                                                                                                                                  |
|            /     /  /            3       /     2\\      /        2\                3       /     2\                                                                                                   | |            /     /  /            3       /     2\\      /        2\                3       /     2\  /          ___\                                                                                                                  | |            /     /  /            3       /     2\\      /        2\                3       /     2\  /          ___\                                                                                                                  |
|           /    \/   \-27*b - 25*b  - 9*b*\1 + b //  - 4*\-3 - 2*b /     27*b   25*b    9*b*\1 + b /                                                                                                   | |           /    \/   \-27*b - 25*b  - 9*b*\1 + b //  - 4*\-3 - 2*b /     27*b   25*b    9*b*\1 + b /  |  1   I*\/ 3 |                                                                                                                  | |           /    \/   \-27*b - 25*b  - 9*b*\1 + b //  - 4*\-3 - 2*b /     27*b   25*b    9*b*\1 + b /  |  1   I*\/ 3 |                                                                                                                  |
|        3 /     ------------------------------------------------------ - ---- - ----- - ------------                                                       2                                           | |        3 /     ------------------------------------------------------ - ---- - ----- - ------------ *|- - - -------|                                                              2                                                   | |        3 /     ------------------------------------------------------ - ---- - ----- - ------------ *|- - + -------|                                                              2                                                   |
|    b   \/                                2                               2       2          2                                                     -3 - 2*b                                            | |    b   \/                                2                               2       2          2        \  2      2   /                                                      -3 - 2*b                                                    | |    b   \/                                2                               2       2          2        \  2      2   /                                                      -3 - 2*b                                                    |
|a + - + --------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------|*|a + - + ------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------|*|a + - + ------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------|
|    3                                                 3                                                          ______________________________________________________________________________________| |    3                                                         3                                                                                  ______________________________________________________________________________________| |    3                                                         3                                                                                  ______________________________________________________________________________________|
|                                                                                                                /     __________________________________________________                               | |                                                                                                                                                /     __________________________________________________                               | |                                                                                                                                                /     __________________________________________________                               |
|                                                                                                               /     /                               2                3                                | |                                                                                                                                               /     /                               2                3                                | |                                                                                                                                               /     /                               2                3                                |
|                                                                                                              /     /  /            3       /     2\\      /        2\                3       /     2\ | |                                                                                                                          /          ___\     /     /  /            3       /     2\\      /        2\                3       /     2\ | |                                                                                                                          /          ___\     /     /  /            3       /     2\\      /        2\                3       /     2\ |
|                                                                                                             /    \/   \-27*b - 25*b  - 9*b*\1 + b //  - 4*\-3 - 2*b /     27*b   25*b    9*b*\1 + b / | |                                                                                                                          |  1   I*\/ 3 |    /    \/   \-27*b - 25*b  - 9*b*\1 + b //  - 4*\-3 - 2*b /     27*b   25*b    9*b*\1 + b / | |                                                                                                                          |  1   I*\/ 3 |    /    \/   \-27*b - 25*b  - 9*b*\1 + b //  - 4*\-3 - 2*b /     27*b   25*b    9*b*\1 + b / |
|                                                                                                        3*3 /     ------------------------------------------------------ - ---- - ----- - ------------ | |                                                                                                                        3*|- - - -------|*3 /     ------------------------------------------------------ - ---- - ----- - ------------ | |                                                                                                                        3*|- - + -------|*3 /     ------------------------------------------------------ - ---- - ----- - ------------ |
\                                                                                                          \/                                2                               2       2          2       / \                                                                                                                          \  2      2   / \/                                2                               2       2          2       / \                                                                                                                          \  2      2   / \/                                2                               2       2          2       /

$$\left(a + \left(\frac{b}{3} + \frac{- 2 b^{2} - 3}{3 \sqrt[3]{- \frac{25 b^{3}}{2} - \frac{9 b \left(b^{2} + 1\right)}{2} - \frac{27 b}{2} + \frac{\sqrt{- 4 \left(- 2 b^{2} - 3\right)^{3} + \left(- 25 b^{3} - 9 b \left(b^{2} + 1\right) - 27 b\right)^{2}}}{2}}} + \frac{\sqrt[3]{- \frac{25 b^{3}}{2} - \frac{9 b \left(b^{2} + 1\right)}{2} - \frac{27 b}{2} + \frac{\sqrt{- 4 \left(- 2 b^{2} - 3\right)^{3} + \left(- 25 b^{3} - 9 b \left(b^{2} + 1\right) - 27 b\right)^{2}}}{2}}}{3}\right)\right) \left(a + \left(\frac{b}{3} + \frac{- 2 b^{2} - 3}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{25 b^{3}}{2} - \frac{9 b \left(b^{2} + 1\right)}{2} - \frac{27 b}{2} + \frac{\sqrt{- 4 \left(- 2 b^{2} - 3\right)^{3} + \left(- 25 b^{3} - 9 b \left(b^{2} + 1\right) - 27 b\right)^{2}}}{2}}} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{25 b^{3}}{2} - \frac{9 b \left(b^{2} + 1\right)}{2} - \frac{27 b}{2} + \frac{\sqrt{- 4 \left(- 2 b^{2} - 3\right)^{3} + \left(- 25 b^{3} - 9 b \left(b^{2} + 1\right) - 27 b\right)^{2}}}{2}}}{3}\right)\right) \left(a + \left(\frac{b}{3} + \frac{- 2 b^{2} - 3}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{25 b^{3}}{2} - \frac{9 b \left(b^{2} + 1\right)}{2} - \frac{27 b}{2} + \frac{\sqrt{- 4 \left(- 2 b^{2} - 3\right)^{3} + \left(- 25 b^{3} - 9 b \left(b^{2} + 1\right) - 27 b\right)^{2}}}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{25 b^{3}}{2} - \frac{9 b \left(b^{2} + 1\right)}{2} - \frac{27 b}{2} + \frac{\sqrt{- 4 \left(- 2 b^{2} - 3\right)^{3} + \left(- 25 b^{3} - 9 b \left(b^{2} + 1\right) - 27 b\right)^{2}}}{2}}}{3}\right)\right)$$