Разложить многочлен на множители x^24-y^22

Разложение на множители

                                  /             _____              _____\ /             _____              _____\ /               _____              _____\ /               _____              _____\ /         _____            _____\ /           _____            _____\ /               _____        _____\ /           _____            _____\ /       _____              _____\ /       _____              _____\ /         _____              _____\ /         _____              _____\ /             _____            _____              _____              _____\ /             _____            _____              _____              _____\ /               _____            _____              _____              _____\ /               _____            _____              _____              _____\ /             _____            _____              _____              _____\ /             _____            _____              _____              _____\ /             _____            _____              _____              _____\ /             _____            _____              _____              _____\                              
/         _____\ /         _____\ |      ___ 24/  22        ___ 24/  22 | |      ___ 24/  22        ___ 24/  22 | |        ___ 24/  22        ___ 24/  22 | |        ___ 24/  22        ___ 24/  22 | |      24/  22      ___ 24/  22 | |        24/  22      ___ 24/  22 | |        ___ 24/  22      24/  22 | |        24/  22      ___ 24/  22 | |    24/  22        ___ 24/  22 | |    24/  22        ___ 24/  22 | |      24/  22        ___ 24/  22 | |      24/  22        ___ 24/  22 | |      ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | |      ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | |        ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | |        ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | |      ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | |      ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | |      ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | |      ___ 24/  22      ___ 24/  22        ___ 24/  22        ___ 24/  22 | /       _____\ /       _____\
|      24/  22 | |      24/  22 | |    \/ 2 *\/  y      I*\/ 2 *\/  y   | |    \/ 2 *\/  y      I*\/ 2 *\/  y   | |      \/ 2 *\/  y      I*\/ 2 *\/  y   | |      \/ 2 *\/  y      I*\/ 2 *\/  y   | |    I*\/  y      \/ 3 *\/  y   | |      I*\/  y      \/ 3 *\/  y   | |      \/ 3 *\/  y      I*\/  y   | |      I*\/  y      \/ 3 *\/  y   | |    \/  y      I*\/ 3 *\/  y   | |    \/  y      I*\/ 3 *\/  y   | |      \/  y      I*\/ 3 *\/  y   | |      \/  y      I*\/ 3 *\/  y   | |    \/ 2 *\/  y      \/ 6 *\/  y      I*\/ 2 *\/  y      I*\/ 6 *\/  y   | |    \/ 2 *\/  y      \/ 6 *\/  y      I*\/ 2 *\/  y      I*\/ 6 *\/  y   | |      \/ 2 *\/  y      \/ 6 *\/  y      I*\/ 2 *\/  y      I*\/ 6 *\/  y   | |      \/ 2 *\/  y      \/ 6 *\/  y      I*\/ 6 *\/  y      I*\/ 2 *\/  y   | |    \/ 2 *\/  y      \/ 6 *\/  y      I*\/ 2 *\/  y      I*\/ 6 *\/  y   | |    \/ 2 *\/  y      \/ 6 *\/  y      I*\/ 6 *\/  y      I*\/ 2 *\/  y   | |    \/ 6 *\/  y      \/ 2 *\/  y      I*\/ 2 *\/  y      I*\/ 6 *\/  y   | |    \/ 6 *\/  y      \/ 2 *\/  y      I*\/ 2 *\/  y      I*\/ 6 *\/  y   | |    24/  22 | |    24/  22 |
\x + I*\/  y   /*\x - I*\/  y   /*|x + -------------- + ----------------|*|x + -------------- - ----------------|*|x + - -------------- + ----------------|*|x + - -------------- - ----------------|*|x + ---------- + --------------|*|x + - ---------- + --------------|*|x + - -------------- + ----------|*|x + - ---------- - --------------|*|x + -------- + ----------------|*|x + -------- - ----------------|*|x + - -------- + ----------------|*|x + - -------- - ----------------|*|x + -------------- - -------------- - ---------------- - ----------------|*|x + -------------- - -------------- + ---------------- + ----------------|*|x + - -------------- - -------------- + ---------------- - ----------------|*|x + - -------------- - -------------- + ---------------- - ----------------|*|x + -------------- + -------------- + ---------------- - ----------------|*|x + -------------- + -------------- + ---------------- - ----------------|*|x + -------------- - -------------- - ---------------- - ----------------|*|x + -------------- - -------------- + ---------------- + ----------------|*\x + \/  y   /*\x - \/  y   /
                                  \          2                 2        / \          2                 2        / \            2                 2        / \            2                 2        / \        2              2       / \          2              2       / \            2              2     / \          2              2       / \       2              2        / \       2              2        / \         2              2        / \         2              2        / \          4                4                 4                  4        / \          4                4                 4                  4        / \            4                4                 4                  4        / \            4                4                 4                  4        / \          4                4                 4                  4        / \          4                4                 4                  4        / \          4                4                 4                  4        / \          4                4                 4                  4        /                              

$$\left(x - i \sqrt[24]{y^{22}}\right) \left(x + i \sqrt[24]{y^{22}}\right) \left(x + \left(\frac{\sqrt{2} \sqrt[24]{y^{22}}}{2} + \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{2} \sqrt[24]{y^{22}}}{2} - \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[24]{y^{22}}}{2} + \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[24]{y^{22}}}{2} - \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{3} \sqrt[24]{y^{22}}}{2} + \frac{i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{3} \sqrt[24]{y^{22}}}{2} - \frac{i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3} \sqrt[24]{y^{22}}}{2} + \frac{i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3} \sqrt[24]{y^{22}}}{2} - \frac{i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(\frac{\sqrt[24]{y^{22}}}{2} + \frac{\sqrt{3} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(\frac{\sqrt[24]{y^{22}}}{2} - \frac{\sqrt{3} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[24]{y^{22}}}{2} + \frac{\sqrt{3} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[24]{y^{22}}}{2} - \frac{\sqrt{3} i \sqrt[24]{y^{22}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \left(\frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \left(\frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4} - \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{2} i \sqrt[24]{y^{22}}}{4} + \frac{\sqrt{6} i \sqrt[24]{y^{22}}}{4}\right)\right) \left(x + \sqrt[24]{y^{22}}\right) \left(x - \sqrt[24]{y^{22}}\right)$$

Комбинаторика

/ 12    11\ / 12    11\
\x   + y  /*\x   - y  /

$$\left(x^{12} - y^{11}\right) \left(x^{12} + y^{11}\right)$$