Разложить многочлен на множители a^16-16

Комбинаторика

/      4\ /     4\ /     4      2\ /     4      2\
\-2 + a /*\2 + a /*\2 + a  - 2*a /*\2 + a  + 2*a /

$$\left(a^{4} - 2\right) \left(a^{4} + 2\right) \left(a^{4} - 2 a^{2} + 2\right) \left(a^{4} + 2 a^{2} + 2\right)$$

Разложение на множители

                                                                                                                                        /               ___________                ___________\ /               ___________                ___________\ /                 ___________                ___________\ /                 ___________                ___________\ /               ___________                ___________\ /               ___________                ___________\ /                 ___________                ___________\ /                 ___________                ___________\
                                                    /     3/4      3/4\ /     3/4      3/4\ /       3/4      3/4\ /       3/4      3/4\ |              /       ___                /       ___ | |              /       ___                /       ___ | |                /       ___                /       ___ | |                /       ___                /       ___ | |              /       ___                /       ___ | |              /       ___                /       ___ | |                /       ___                /       ___ | |                /       ___                /       ___ |
/    4 ___\ /    4 ___\ /      4 ___\ /      4 ___\ |    2      I*2   | |    2      I*2   | |      2      I*2   | |      2      I*2   | |    4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  | |    4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  | |      4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  | |      4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  | |    4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  | |    4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  | |      4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  | |      4 ___    /  1   \/ 2       4 ___    /  1   \/ 2  |
\a + \/ 2 /*\a - \/ 2 /*\a + I*\/ 2 /*\a - I*\/ 2 /*|a + ---- + ------|*|a + ---- - ------|*|a + - ---- + ------|*|a + - ---- - ------|*|a + \/ 2 *  /   - - -----  + I*\/ 2 *  /   - + ----- |*|a + \/ 2 *  /   - - -----  - I*\/ 2 *  /   - + ----- |*|a + - \/ 2 *  /   - - -----  + I*\/ 2 *  /   - + ----- |*|a + - \/ 2 *  /   - - -----  - I*\/ 2 *  /   - + ----- |*|a + \/ 2 *  /   - + -----  + I*\/ 2 *  /   - - ----- |*|a + \/ 2 *  /   - + -----  - I*\/ 2 *  /   - - ----- |*|a + - \/ 2 *  /   - + -----  + I*\/ 2 *  /   - - ----- |*|a + - \/ 2 *  /   - + -----  - I*\/ 2 *  /   - - ----- |
                                                    \     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   /

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