Общий множитель 128*a^7+b^7

Комбинаторика

          / 6       6         5      3  3        5      2  4       4  2\
(b + 2*a)*\b  + 64*a  - 32*b*a  - 8*a *b  - 2*a*b  + 4*a *b  + 16*a *b /

$$\left(2 a + b\right) \left(64 a^{6} - 32 a^{5} b + 16 a^{4} b^{2} - 8 a^{3} b^{3} + 4 a^{2} b^{4} - 2 a b^{5} + b^{6}\right)$$

Разложение на множители

/      /   /pi\        /pi\\\ /      /     2/pi\      2/pi\\\ /      /   2/pi\      2/pi\                    \\ /      /   /pi\    /2*pi\      /pi\    /2*pi\        /pi\    /2*pi\        /2*pi\    /pi\\\ /      /   /pi\    /2*pi\      /pi\    /2*pi\        /2*pi\    /pi\        /pi\    /2*pi\\\ /      /     /pi\    /3*pi\      /pi\    /3*pi\        /pi\    /3*pi\        /3*pi\    /pi\\\ /      /   /pi\    /3*pi\      /pi\    /3*pi\        /pi\    /3*pi\        /3*pi\    /pi\\\
|      |cos|--|   I*sin|--||| |      |  cos |--|   sin |--||| |      |sin |--|   cos |--|                    || |      |cos|--|*cos|----|   sin|--|*sin|----|   I*cos|--|*sin|----|   I*cos|----|*sin|--||| |      |cos|--|*cos|----|   sin|--|*sin|----|   I*cos|----|*sin|--|   I*cos|--|*sin|----||| |      |  cos|--|*cos|----|   sin|--|*sin|----|   I*cos|--|*sin|----|   I*cos|----|*sin|--||| |      |sin|--|*sin|----|   cos|--|*cos|----|   I*cos|--|*sin|----|   I*cos|----|*sin|--|||
|      |   \7 /        \7 /|| |      |      \7 /       \7 /|| |      |    \7 /       \7 /        /pi\    /pi\|| |      |   \7 /    \ 7  /      \7 /    \ 7  /        \7 /    \ 7  /        \ 7  /    \7 /|| |      |   \7 /    \ 7  /      \7 /    \ 7  /        \ 7  /    \7 /        \7 /    \ 7  /|| |      |     \7 /    \ 7  /      \7 /    \ 7  /        \7 /    \ 7  /        \ 7  /    \7 /|| |      |   \7 /    \ 7  /      \7 /    \ 7  /        \7 /    \ 7  /        \ 7  /    \7 /||
|a - b*|------- + ---------||*|a - b*|- -------- - --------||*|a - b*|-------- - -------- - I*cos|--|*sin|--|||*|a - b*|----------------- - ----------------- + ------------------- + -------------------||*|a - b*|----------------- + ----------------- + ------------------- - -------------------||*|a - b*|- ----------------- - ----------------- + ------------------- - -------------------||*|a - b*|----------------- - ----------------- - ------------------- - -------------------||
\      \   2          2    // \      \     2          2    // \      \   2          2            \7 /    \7 /// \      \        2                   2                    2                     2         // \      \        2                   2                    2                     2         // \      \          2                   2                    2                     2         // \      \        2                   2                    2                     2         //

$$\left(a - b \left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{7} \right)}}{2}\right)\right) \left(a - b \left(- \frac{\cos^{2}{\left(\frac{\pi}{7} \right)}}{2} - \frac{\sin^{2}{\left(\frac{\pi}{7} \right)}}{2}\right)\right) \left(a - b \left(- \frac{\cos^{2}{\left(\frac{\pi}{7} \right)}}{2} + \frac{\sin^{2}{\left(\frac{\pi}{7} \right)}}{2} - i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(a - b \left(- \frac{\sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2} + \frac{i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2}\right)\right) \left(a - b \left(\frac{\sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2} - \frac{i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2}\right)\right) \left(a - b \left(- \frac{\sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)}}{2} - \frac{\cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2} - \frac{i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2} + \frac{i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2}\right)\right) \left(a - b \left(- \frac{\cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2} + \frac{\sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)}}{2} - \frac{i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2} - \frac{i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2}\right)\right)$$