Разложить многочлен на множители 216*a^9*b^15+1

Комбинаторика

/       3  5\ /       3  5       6  10\
\1 + 6*a *b /*\1 - 6*a *b  + 36*a *b  /

$$\left(6 a^{3} b^{5} + 1\right) \left(36 a^{6} b^{10} - 6 a^{3} b^{5} + 1\right)$$

Разложение на множители

/              _____\ /              _____                     _____\ /              _____                     _____\ /              _____                       _____        \ /              _____                       _____        \ /                _____                         _____          \ /                _____                         _____          \ /                _____                         _____          \ /                _____                         _____          \
|     2/3     / -1  | |     2/3     / -1        2/3 6 ___     / -1  | |     2/3     / -1        2/3 6 ___     / -1  | |     2/3     / -1      /pi\      2/3     / -1      /pi\| |     2/3     / -1      /pi\      2/3     / -1      /pi\| |       2/3     / -1      /2*pi\      2/3     / -1      /2*pi\| |       2/3     / -1      /2*pi\      2/3     / -1      /2*pi\| |       2/3     / -1      /4*pi\      2/3     / -1      /4*pi\| |       2/3     / -1      /4*pi\      2/3     / -1      /4*pi\|
|    6   *   /  --- | |    6   *   /  ---    I*2   *\/ 3 *   /  --- | |    6   *   /  ---    I*2   *\/ 3 *   /  --- | |    6   *   /  --- *cos|--|   I*6   *   /  --- *sin|--|| |    6   *   /  --- *cos|--|   I*6   *   /  --- *sin|--|| |      6   *   /  --- *cos|----|   I*6   *   /  --- *sin|----|| |      6   *   /  --- *cos|----|   I*6   *   /  --- *sin|----|| |      6   *   /  --- *cos|----|   I*6   *   /  --- *sin|----|| |      6   *   /  --- *cos|----|   I*6   *   /  --- *sin|----||
|         9 /    15 | |         9 /    15                 9 /    15 | |         9 /    15                 9 /    15 | |         9 /    15     \9 /          9 /    15     \9 /| |         9 /    15     \9 /          9 /    15     \9 /| |           9 /    15     \ 9  /          9 /    15     \ 9  /| |           9 /    15     \ 9  /          9 /    15     \ 9  /| |           9 /    15     \ 9  /          9 /    15     \ 9  /| |           9 /    15     \ 9  /          9 /    15     \ 9  /|
|         \/    b   | |         \/    b                   \/    b   | |         \/    b                   \/    b   | |         \/    b                     \/    b           | |         \/    b                     \/    b           | |           \/    b                       \/    b             | |           \/    b                       \/    b             | |           \/    b                       \/    b             | |           \/    b                       \/    b             |
|a - ---------------|*|a + --------------- + -----------------------|*|a + --------------- - -----------------------|*|a + ----------------------- + -------------------------|*|a + ----------------------- - -------------------------|*|a + - ------------------------- + ---------------------------|*|a + - ------------------------- - ---------------------------|*|a + - ------------------------- + ---------------------------|*|a + - ------------------------- - ---------------------------|
\           6       / \           12                    4           / \           12                    4           / \               6                          6            / \               6                          6            / \                  6                            6             / \                  6                            6             / \                  6                            6             / \                  6                            6             /

$$\left(a - \frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}}}{6}\right) \left(a + \left(\frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}}}{12} + \frac{2^{\frac{2}{3}} \sqrt[6]{3} i \sqrt[9]{- \frac{1}{b^{15}}}}{4}\right)\right) \left(a + \left(\frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}}}{12} - \frac{2^{\frac{2}{3}} \sqrt[6]{3} i \sqrt[9]{- \frac{1}{b^{15}}}}{4}\right)\right) \left(a + \left(\frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}} \cos{\left(\frac{\pi}{9} \right)}}{6} + \frac{6^{\frac{2}{3}} i \sqrt[9]{- \frac{1}{b^{15}}} \sin{\left(\frac{\pi}{9} \right)}}{6}\right)\right) \left(a + \left(\frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}} \cos{\left(\frac{\pi}{9} \right)}}{6} - \frac{6^{\frac{2}{3}} i \sqrt[9]{- \frac{1}{b^{15}}} \sin{\left(\frac{\pi}{9} \right)}}{6}\right)\right) \left(a + \left(- \frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}} \cos{\left(\frac{2 \pi}{9} \right)}}{6} + \frac{6^{\frac{2}{3}} i \sqrt[9]{- \frac{1}{b^{15}}} \sin{\left(\frac{2 \pi}{9} \right)}}{6}\right)\right) \left(a + \left(- \frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}} \cos{\left(\frac{2 \pi}{9} \right)}}{6} - \frac{6^{\frac{2}{3}} i \sqrt[9]{- \frac{1}{b^{15}}} \sin{\left(\frac{2 \pi}{9} \right)}}{6}\right)\right) \left(a + \left(- \frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}} \cos{\left(\frac{4 \pi}{9} \right)}}{6} + \frac{6^{\frac{2}{3}} i \sqrt[9]{- \frac{1}{b^{15}}} \sin{\left(\frac{4 \pi}{9} \right)}}{6}\right)\right) \left(a + \left(- \frac{6^{\frac{2}{3}} \sqrt[9]{- \frac{1}{b^{15}}} \cos{\left(\frac{4 \pi}{9} \right)}}{6} - \frac{6^{\frac{2}{3}} i \sqrt[9]{- \frac{1}{b^{15}}} \sin{\left(\frac{4 \pi}{9} \right)}}{6}\right)\right)$$