Разложить многочлен на множители x^16-y^10

Комбинаторика

/ 8    5\ / 8    5\
\x  + y /*\x  - y /

$$\left(x^{8} - y^{5}\right) \left(x^{8} + y^{5}\right)$$

Разложение на множители

                                  /             _____              _____\ /             _____              _____\ /               _____              _____\ /               _____              _____\ /                  ___________                   ___________\ /                  ___________                   ___________\ /                    ___________                   ___________\ /                    ___________                   ___________\ /                  ___________                   ___________\ /                  ___________                   ___________\ /                    ___________                   ___________\ /                    ___________                   ___________\                              
/         _____\ /         _____\ |      ___ 16/  10        ___ 16/  10 | |      ___ 16/  10        ___ 16/  10 | |        ___ 16/  10        ___ 16/  10 | |        ___ 16/  10        ___ 16/  10 | |       _____     /       ___         _____     /       ___ | |       _____     /       ___         _____     /       ___ | |         _____     /       ___         _____     /       ___ | |         _____     /       ___         _____     /       ___ | |       _____     /       ___         _____     /       ___ | |       _____     /       ___         _____     /       ___ | |         _____     /       ___         _____     /       ___ | |         _____     /       ___         _____     /       ___ | /       _____\ /       _____\
|      16/  10 | |      16/  10 | |    \/ 2 *\/  y      I*\/ 2 *\/  y   | |    \/ 2 *\/  y      I*\/ 2 *\/  y   | |      \/ 2 *\/  y      I*\/ 2 *\/  y   | |      \/ 2 *\/  y      I*\/ 2 *\/  y   | |    16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |    16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |      16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |      16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |    16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |    16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |      16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |      16/  10     /  1   \/ 2       16/  10     /  1   \/ 2  | |    16/  10 | |    16/  10 |
\x + I*\/  y   /*\x - I*\/  y   /*|x + -------------- + ----------------|*|x + -------------- - ----------------|*|x + - -------------- + ----------------|*|x + - -------------- - ----------------|*|x + \/  y   *  /   - - -----  + I*\/  y   *  /   - + ----- |*|x + \/  y   *  /   - - -----  - I*\/  y   *  /   - + ----- |*|x + - \/  y   *  /   - - -----  + I*\/  y   *  /   - + ----- |*|x + - \/  y   *  /   - - -----  - I*\/  y   *  /   - + ----- |*|x + \/  y   *  /   - + -----  + I*\/  y   *  /   - - ----- |*|x + \/  y   *  /   - + -----  - I*\/  y   *  /   - - ----- |*|x + - \/  y   *  /   - + -----  + I*\/  y   *  /   - - ----- |*|x + - \/  y   *  /   - + -----  - I*\/  y   *  /   - - ----- |*\x + \/  y   /*\x - \/  y   /
                                  \          2                 2        / \          2                 2        / \            2                 2        / \            2                 2        / \             \/    2     4                 \/    2     4   / \             \/    2     4                 \/    2     4   / \               \/    2     4                 \/    2     4   / \               \/    2     4                 \/    2     4   / \             \/    2     4                 \/    2     4   / \             \/    2     4                 \/    2     4   / \               \/    2     4                 \/    2     4   / \               \/    2     4                 \/    2     4   /                              

$$\left(x - i \sqrt[16]{y^{10}}\right) \left(x + i \sqrt[16]{y^{10}}\right) \left(x + \left(\frac{\sqrt{2} \sqrt[16]{y^{10}}}{2} + \frac{\sqrt{2} i \sqrt[16]{y^{10}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{2} \sqrt[16]{y^{10}}}{2} - \frac{\sqrt{2} i \sqrt[16]{y^{10}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[16]{y^{10}}}{2} + \frac{\sqrt{2} i \sqrt[16]{y^{10}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[16]{y^{10}}}{2} - \frac{\sqrt{2} i \sqrt[16]{y^{10}}}{2}\right)\right) \left(x + \left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}} + i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}}\right)\right) \left(x + \left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}} - i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}}\right)\right) \left(x + \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}} + i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}}\right)\right) \left(x + \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}} - i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}}\right)\right) \left(x + \left(\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}} + i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}}\right)\right) \left(x + \left(\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}} - i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}}\right)\right) \left(x + \left(- \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}} + i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}}\right)\right) \left(x + \left(- \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt[16]{y^{10}} - i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt[16]{y^{10}}\right)\right) \left(x + \sqrt[16]{y^{10}}\right) \left(x - \sqrt[16]{y^{10}}\right)$$