Общий множитель 11*a^8+a^15

Комбинаторика

 8 /      7\
a *\11 + a /

$$a^{8} \left(a^{7} + 11\right)$$

Разложение на множители

  /      7 ____    /pi\     7 ____    /pi\\ /    7 ____    2/pi\   7 ____    2/pi\\ /      7 ____    2/pi\   7 ____    2/pi\       7 ____    /pi\    /pi\\ /      7 ____    /pi\    /2*pi\   7 ____    /pi\    /2*pi\     7 ____    /pi\    /2*pi\     7 ____    /2*pi\    /pi\\ /      7 ____    /pi\    /2*pi\   7 ____    /pi\    /2*pi\     7 ____    /2*pi\    /pi\     7 ____    /pi\    /2*pi\\ /    7 ____    /pi\    /3*pi\   7 ____    /pi\    /3*pi\     7 ____    /pi\    /3*pi\     7 ____    /3*pi\    /pi\\ /      7 ____    /pi\    /3*pi\   7 ____    /pi\    /3*pi\     7 ____    /pi\    /3*pi\     7 ____    /3*pi\    /pi\\
a*|a + - \/ 11 *cos|--| - I*\/ 11 *sin|--||*|a + \/ 11 *cos |--| + \/ 11 *sin |--||*|a + - \/ 11 *sin |--| + \/ 11 *cos |--| + 2*I*\/ 11 *cos|--|*sin|--||*|a + - \/ 11 *cos|--|*cos|----| + \/ 11 *sin|--|*sin|----| - I*\/ 11 *cos|--|*sin|----| - I*\/ 11 *cos|----|*sin|--||*|a + - \/ 11 *cos|--|*cos|----| - \/ 11 *sin|--|*sin|----| - I*\/ 11 *cos|----|*sin|--| + I*\/ 11 *cos|--|*sin|----||*|a + \/ 11 *cos|--|*cos|----| + \/ 11 *sin|--|*sin|----| - I*\/ 11 *cos|--|*sin|----| + I*\/ 11 *cos|----|*sin|--||*|a + - \/ 11 *sin|--|*sin|----| + \/ 11 *cos|--|*cos|----| + I*\/ 11 *cos|--|*sin|----| + I*\/ 11 *cos|----|*sin|--||
  \                \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 // \                \7 /    \ 7  /             \7 /    \ 7  /               \7 /    \ 7  /               \ 7  /    \7 //

$$a \left(a + \left(- \sqrt[7]{11} \cos{\left(\frac{\pi}{7} \right)} - \sqrt[7]{11} i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(a + \left(\sqrt[7]{11} \sin^{2}{\left(\frac{\pi}{7} \right)} + \sqrt[7]{11} \cos^{2}{\left(\frac{\pi}{7} \right)}\right)\right) \left(a + \left(- \sqrt[7]{11} \sin^{2}{\left(\frac{\pi}{7} \right)} + \sqrt[7]{11} \cos^{2}{\left(\frac{\pi}{7} \right)} + 2 \sqrt[7]{11} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(a + \left(- \sqrt[7]{11} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + \sqrt[7]{11} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - \sqrt[7]{11} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} - \sqrt[7]{11} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(a + \left(- \sqrt[7]{11} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} - \sqrt[7]{11} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - \sqrt[7]{11} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + \sqrt[7]{11} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(a + \left(\sqrt[7]{11} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{11} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} - \sqrt[7]{11} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} + \sqrt[7]{11} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}\right)\right) \left(a + \left(- \sqrt[7]{11} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{11} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{11} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{11} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right)$$

Объединение рациональных выражений

 8 /      7\
a *\11 + a /

$$a^{8} \left(a^{7} + 11\right)$$

Общее упрощение

 8 /      7\
a *\11 + a /

$$a^{8} \left(a^{7} + 11\right)$$