Mister Exam

# Factor polynomial x^7+y^7

An expression to simplify:

### The solution

You have entered [src]
 7    7
x  + y 
$$x^{7} + y^{7}$$
x^7 + y^7
Factorization [src]
/      /     /pi\      /pi\\\ /      /     2/pi\      2/pi\\\ /      /   2/pi\      2/pi\          /pi\    /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\\\
|x - y*|I*sin|--| + cos|--|||*|x - y*|- cos |--| - sin |--|||*|x - y*|sin |--| - cos |--| - 2*I*cos|--|*sin|--|||*|x - y*|cos|--|*cos|----| - sin|--|*sin|----| + I*cos|--|*sin|----| + I*cos|----|*sin|--|||*|x - y*|cos|--|*cos|----| + sin|--|*sin|----| + I*cos|----|*sin|--| - I*cos|--|*sin|----|||*|x - y*|- cos|--|*cos|----| - sin|--|*sin|----| + I*cos|--|*sin|----| - I*cos|----|*sin|--|||*|x - y*|sin|--|*sin|----| - cos|--|*cos|----| - I*cos|--|*sin|----| - I*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 ///
$$\left(x - y \left(\cos{\left(\frac{\pi}{7} \right)} + i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(x - y \left(- \cos^{2}{\left(\frac{\pi}{7} \right)} - \sin^{2}{\left(\frac{\pi}{7} \right)}\right)\right) \left(x - y \left(- \cos^{2}{\left(\frac{\pi}{7} \right)} + \sin^{2}{\left(\frac{\pi}{7} \right)} - 2 i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x - y \left(- \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x - y \left(\sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} + \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} - i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} + i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x - y \left(- \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} - \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} - i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x - y \left(- \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} - i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} - i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}\right)\right)$$
((((((x - y*(i*sin(pi/7) + cos(pi/7)))*(x - y*(-cos(pi/7)^2 - sin(pi/7)^2)))*(x - y*(sin(pi/7)^2 - cos(pi/7)^2 - 2*i*cos(pi/7)*sin(pi/7))))*(x - y*(cos(pi/7)*cos(2*pi/7) - sin(pi/7)*sin(2*pi/7) + i*cos(pi/7)*sin(2*pi/7) + i*cos(2*pi/7)*sin(pi/7))))*(x - y*(cos(pi/7)*cos(2*pi/7) + sin(pi/7)*sin(2*pi/7) + i*cos(2*pi/7)*sin(pi/7) - i*cos(pi/7)*sin(2*pi/7))))*(x - y*(-cos(pi/7)*cos(3*pi/7) - sin(pi/7)*sin(3*pi/7) + i*cos(pi/7)*sin(3*pi/7) - i*cos(3*pi/7)*sin(pi/7))))*(x - y*(sin(pi/7)*sin(3*pi/7) - cos(pi/7)*cos(3*pi/7) - i*cos(pi/7)*sin(3*pi/7) - i*cos(3*pi/7)*sin(pi/7)))
x^7 + y^7
x^7 + y^7
        / 6    6    2  4    4  2      5      5    3  3\
(x + y)*\x  + y  + x *y  + x *y  - x*y  - y*x  - x *y /
$$\left(x + y\right) \left(x^{6} - x^{5} y + x^{4} y^{2} - x^{3} y^{3} + x^{2} y^{4} - x y^{5} + y^{6}\right)$$
(x + y)*(x^6 + y^6 + x^2*y^4 + x^4*y^2 - x*y^5 - y*x^5 - x^3*y^3)