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Simplificación de expresiones/ Descomposición de multiplicadores/ x^9-y^9

Factorizar el polinomio x^9-y^9

Expresión a simplificar:

Solución

Ha introducido [src] 
 9    9
x  - y
$$x^{9} - y^{9}$$ 
x^9 - y^9
Factorización [src] 
        /      /          ___\\ /      /          ___\\                                                                                                                                                                                                            
        |      |  1   I*\/ 3 || |      |  1   I*\/ 3 || /      /     /pi\        /pi\\\ /      /     /pi\        /pi\\\ /      /       /2*pi\      /2*pi\\\ /      /     /2*pi\      /2*pi\\\ /      /       /4*pi\      /4*pi\\\ /      /     /4*pi\      /4*pi\\\
(x - y)*|x - y*|- - - -------||*|x - y*|- - + -------||*|x - y*|- cos|--| - I*sin|--|||*|x - y*|- cos|--| + I*sin|--|||*|x - y*|- I*sin|----| + cos|----|||*|x - y*|I*sin|----| + cos|----|||*|x - y*|- I*sin|----| + cos|----|||*|x - y*|I*sin|----| + cos|----|||
        \      \  2      2   // \      \  2      2   // \      \     \9 /        \9 /// \      \     \9 /        \9 /// \      \       \ 9  /      \ 9  /// \      \     \ 9  /      \ 9  /// \      \       \ 9  /      \ 9  /// \      \     \ 9  /      \ 9  ///
$$\left(x - y\right) \left(x - y \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x - y \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x - y \left(- \cos{\left(\frac{\pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(x - y \left(- \cos{\left(\frac{\pi}{9} \right)} + i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(x - y \left(\cos{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x - y \left(\cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x - y \left(\cos{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x - y \left(\cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right)$$ 
((((((((x - y)*(x - y*(-1/2 - i*sqrt(3)/2)))*(x - y*(-1/2 + i*sqrt(3)/2)))*(x - y*(-cos(pi/9) - i*sin(pi/9))))*(x - y*(-cos(pi/9) + i*sin(pi/9))))*(x - y*(-i*sin(2*pi/9) + cos(2*pi/9))))*(x - y*(i*sin(2*pi/9) + cos(2*pi/9))))*(x - y*(-i*sin(4*pi/9) + cos(4*pi/9))))*(x - y*(i*sin(4*pi/9) + cos(4*pi/9)))
Respuesta numérica [src] 
x^9 - y^9
x^9 - y^9
Combinatoria [src] 
        / 2    2      \ / 6    6    3  3\
(x - y)*\x  + y  + x*y/*\x  + y  + x *y /
$$\left(x - y\right) \left(x^{2} + x y + y^{2}\right) \left(x^{6} + x^{3} y^{3} + y^{6}\right)$$ 
(x - y)*(x^2 + y^2 + x*y)*(x^6 + y^6 + x^3*y^3)
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