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Simplificación de expresiones/ Descomposición de multiplicadores/ a^9+b^9

Factorizar el polinomio a^9+b^9

Expresión a simplificar:

Solución

Ha introducido [src] 
 9    9
a  + b
a9+b9a^{9} + b^{9} 
a^9 + b^9
Factorización [src] 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /      /     /pi\        /pi\     ___    /pi\       ___    /pi\\\ /      /     /pi\     ___    /pi\        /pi\       ___    /pi\\\
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |      |  cos|--|   I*sin|--|   \/ 3 *sin|--|   I*\/ 3 *cos|--||| |      |  cos|--|   \/ 3 *sin|--|   I*sin|--|   I*\/ 3 *cos|--|||
/      /     /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\    /4*pi\      /pi\    /4*pi\        /pi\    /4*pi\        /4*pi\    /pi\\\ /      /   /pi\    /4*pi\      /pi\    /4*pi\        /4*pi\    /pi\        /pi\    /4*pi\\\ |      |     \9 /        \9 /            \9 /              \9 /|| |      |     \9 /            \9 /        \9 /              \9 /||
|a - b*|I*sin|--| + cos|--|||*|a - b*|- cos |--| - sin |--|||*|a - b*|sin |--| - cos |--| - 2*I*cos|--|*sin|--|||*|a - b*|cos|--|*cos|----| - sin|--|*sin|----| + I*cos|--|*sin|----| + I*cos|----|*sin|--|||*|a - b*|cos|--|*cos|----| + sin|--|*sin|----| + I*cos|----|*sin|--| - I*cos|--|*sin|----|||*|a - b*|cos|--|*cos|----| - sin|--|*sin|----| + I*cos|--|*sin|----| + I*cos|----|*sin|--|||*|a - b*|cos|--|*cos|----| + sin|--|*sin|----| + I*cos|----|*sin|--| - I*cos|--|*sin|----|||*|a - b*|- ------- - --------- - ------------- + ---------------||*|a - b*|- ------- + ------------- - --------- - ---------------||
\      \     \9 /      \9 /// \      \      \9 /       \9 /// \      \    \9 /       \9 /          \9 /    \9 /// \      \   \9 /    \ 9  /      \9 /    \ 9  /        \9 /    \ 9  /        \ 9  /    \9 /// \      \   \9 /    \ 9  /      \9 /    \ 9  /        \ 9  /    \9 /        \9 /    \ 9  /// \      \   \9 /    \ 9  /      \9 /    \ 9  /        \9 /    \ 9  /        \ 9  /    \9 /// \      \   \9 /    \ 9  /      \9 /    \ 9  /        \ 9  /    \9 /        \9 /    \ 9  /// \      \     2          2             2                2       // \      \     2            2             2              2       //
(a−b(cos⁡(π9)+isin⁡(π9)))(a−b(−cos⁡2(π9)−sin⁡2(π9)))(a−b(−cos⁡2(π9)+sin⁡2(π9)−2isin⁡(π9)cos⁡(π9)))(a−b(−sin⁡(π9)sin⁡(2π9)+cos⁡(π9)cos⁡(2π9)+isin⁡(π9)cos⁡(2π9)+isin⁡(2π9)cos⁡(π9)))(a−b(sin⁡(π9)sin⁡(2π9)+cos⁡(π9)cos⁡(2π9)−isin⁡(2π9)cos⁡(π9)+isin⁡(π9)cos⁡(2π9)))(a−b(−sin⁡(π9)sin⁡(4π9)+cos⁡(π9)cos⁡(4π9)+isin⁡(π9)cos⁡(4π9)+isin⁡(4π9)cos⁡(π9)))(a−b(cos⁡(π9)cos⁡(4π9)+sin⁡(π9)sin⁡(4π9)−isin⁡(4π9)cos⁡(π9)+isin⁡(π9)cos⁡(4π9)))(a−b(−cos⁡(π9)2−3sin⁡(π9)2−isin⁡(π9)2+3icos⁡(π9)2))(a−b(−cos⁡(π9)2+3sin⁡(π9)2−3icos⁡(π9)2−isin⁡(π9)2))\left(a - b \left(\cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(a - b \left(- \cos^{2}{\left(\frac{\pi}{9} \right)} - \sin^{2}{\left(\frac{\pi}{9} \right)}\right)\right) \left(a - b \left(- \cos^{2}{\left(\frac{\pi}{9} \right)} + \sin^{2}{\left(\frac{\pi}{9} \right)} - 2 i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(a - b \left(- \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(a - b \left(\sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(a - b \left(- \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(a - b \left(\cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(a - b \left(- \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} - \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(a - b \left(- \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2}\right)\right) 
((((((((a - b*(i*sin(pi/9) + cos(pi/9)))*(a - b*(-cos(pi/9)^2 - sin(pi/9)^2)))*(a - b*(sin(pi/9)^2 - cos(pi/9)^2 - 2*i*cos(pi/9)*sin(pi/9))))*(a - b*(cos(pi/9)*cos(2*pi/9) - sin(pi/9)*sin(2*pi/9) + i*cos(pi/9)*sin(2*pi/9) + i*cos(2*pi/9)*sin(pi/9))))*(a - b*(cos(pi/9)*cos(2*pi/9) + sin(pi/9)*sin(2*pi/9) + i*cos(2*pi/9)*sin(pi/9) - i*cos(pi/9)*sin(2*pi/9))))*(a - b*(cos(pi/9)*cos(4*pi/9) - sin(pi/9)*sin(4*pi/9) + i*cos(pi/9)*sin(4*pi/9) + i*cos(4*pi/9)*sin(pi/9))))*(a - b*(cos(pi/9)*cos(4*pi/9) + sin(pi/9)*sin(4*pi/9) + i*cos(4*pi/9)*sin(pi/9) - i*cos(pi/9)*sin(4*pi/9))))*(a - b*(-cos(pi/9)/2 - i*sin(pi/9)/2 - sqrt(3)*sin(pi/9)/2 + i*sqrt(3)*cos(pi/9)/2)))*(a - b*(-cos(pi/9)/2 + sqrt(3)*sin(pi/9)/2 - i*sin(pi/9)/2 - i*sqrt(3)*cos(pi/9)/2))
Respuesta numérica [src] 
a^9 + b^9
a^9 + b^9
Combinatoria [src] 
        / 2    2      \ / 6    6    3  3\
(a + b)*\a  + b  - a*b/*\a  + b  - a *b /
(a+b)(a2−ab+b2)(a6−a3b3+b6)\left(a + b\right) \left(a^{2} - a b + b^{2}\right) \left(a^{6} - a^{3} b^{3} + b^{6}\right) 
(a + b)*(a^2 + b^2 - a*b)*(a^6 + b^6 - a^3*b^3)
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