Общий множитель 64*x^9-y^3

Комбинаторика

/        3\ / 2       6        3\
\-y + 4*x /*\y  + 16*x  + 4*y*x /

$$\left(4 x^{3} - y\right) \left(16 x^{6} + 4 x^{3} y + y^{2}\right)$$

Разложение на множители

                                                                                                            /             ____                      ____        \ /             ____                      ____        \ /               ____                        ____          \ /               ____                        ____          \ /               ____                        ____          \ /               ____                        ____          \
/             ____\ /             ____                    ____\ /             ____                    ____\ |    3 ___ 9 /  3     /pi\     3 ___ 9 /  3     /pi\| |    3 ___ 9 /  3     /pi\     3 ___ 9 /  3     /pi\| |      3 ___ 9 /  3     /2*pi\     3 ___ 9 /  3     /2*pi\| |      3 ___ 9 /  3     /2*pi\     3 ___ 9 /  3     /2*pi\| |      3 ___ 9 /  3     /4*pi\     3 ___ 9 /  3     /4*pi\| |      3 ___ 9 /  3     /4*pi\     3 ___ 9 /  3     /4*pi\|
|    3 ___ 9 /  3 | |    3 ___ 9 /  3      3 ___   ___ 9 /  3 | |    3 ___ 9 /  3      3 ___   ___ 9 /  3 | |    \/ 2 *\/  y  *cos|--|   I*\/ 2 *\/  y  *sin|--|| |    \/ 2 *\/  y  *cos|--|   I*\/ 2 *\/  y  *sin|--|| |      \/ 2 *\/  y  *cos|----|   I*\/ 2 *\/  y  *sin|----|| |      \/ 2 *\/  y  *cos|----|   I*\/ 2 *\/  y  *sin|----|| |      \/ 2 *\/  y  *cos|----|   I*\/ 2 *\/  y  *sin|----|| |      \/ 2 *\/  y  *cos|----|   I*\/ 2 *\/  y  *sin|----||
|    \/ 2 *\/  y  | |    \/ 2 *\/  y     I*\/ 2 *\/ 3 *\/  y  | |    \/ 2 *\/  y     I*\/ 2 *\/ 3 *\/  y  | |                     \9 /                      \9 /| |                     \9 /                      \9 /| |                       \ 9  /                      \ 9  /| |                       \ 9  /                      \ 9  /| |                       \ 9  /                      \ 9  /| |                       \ 9  /                      \ 9  /|
|x - -------------|*|x + ------------- + ---------------------|*|x + ------------- - ---------------------|*|x + --------------------- + -----------------------|*|x + --------------------- - -----------------------|*|x + - ----------------------- + -------------------------|*|x + - ----------------------- - -------------------------|*|x + - ----------------------- + -------------------------|*|x + - ----------------------- - -------------------------|
\          2      / \          4                   4          / \          4                   4          / \              2                        2           / \              2                        2           / \                 2                          2            / \                 2                          2            / \                 2                          2            / \                 2                          2            /

$$\left(x - \frac{\sqrt[3]{2} \sqrt[9]{y^{3}}}{2}\right) \left(x + \left(\frac{\sqrt[3]{2} \sqrt[9]{y^{3}}}{4} + \frac{\sqrt[3]{2} \sqrt{3} i \sqrt[9]{y^{3}}}{4}\right)\right) \left(x + \left(\frac{\sqrt[3]{2} \sqrt[9]{y^{3}}}{4} - \frac{\sqrt[3]{2} \sqrt{3} i \sqrt[9]{y^{3}}}{4}\right)\right) \left(x + \left(\frac{\sqrt[3]{2} \sqrt[9]{y^{3}} \cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt[3]{2} i \sqrt[9]{y^{3}} \sin{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(x + \left(\frac{\sqrt[3]{2} \sqrt[9]{y^{3}} \cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt[3]{2} i \sqrt[9]{y^{3}} \sin{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[3]{2} \sqrt[9]{y^{3}} \cos{\left(\frac{2 \pi}{9} \right)}}{2} + \frac{\sqrt[3]{2} i \sqrt[9]{y^{3}} \sin{\left(\frac{2 \pi}{9} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[3]{2} \sqrt[9]{y^{3}} \cos{\left(\frac{2 \pi}{9} \right)}}{2} - \frac{\sqrt[3]{2} i \sqrt[9]{y^{3}} \sin{\left(\frac{2 \pi}{9} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[3]{2} \sqrt[9]{y^{3}} \cos{\left(\frac{4 \pi}{9} \right)}}{2} + \frac{\sqrt[3]{2} i \sqrt[9]{y^{3}} \sin{\left(\frac{4 \pi}{9} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt[3]{2} \sqrt[9]{y^{3}} \cos{\left(\frac{4 \pi}{9} \right)}}{2} - \frac{\sqrt[3]{2} i \sqrt[9]{y^{3}} \sin{\left(\frac{4 \pi}{9} \right)}}{2}\right)\right)$$