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Simplificación de expresiones/ Descomposición de multiplicadores/ x^8-y^8

Factorizar el polinomio x^8-y^8

Expresión a simplificar:

Solución

Ha introducido [src] 
 8    8
x  - y
x8−y8x^{8} - y^{8} 
x^8 - y^8
Factorización [src] 
                                    /      /    ___       ___\\ /      /    ___       ___\\ /      /  ___       ___\\ /      /  ___       ___\\
                                    |      |  \/ 2    I*\/ 2 || |      |  \/ 2    I*\/ 2 || |      |\/ 2    I*\/ 2 || |      |\/ 2    I*\/ 2 ||
(x + y)*(x - y)*(x + I*y)*(x - I*y)*|x - y*|- ----- - -------||*|x - y*|- ----- + -------||*|x - y*|----- - -------||*|x - y*|----- + -------||
                                    \      \    2        2   // \      \    2        2   // \      \  2        2   // \      \  2        2   //
(x−y)(x+y)(x+iy)(x−iy)(x−y(−22−2i2))(x−y(−22+2i2))(x−y(22−2i2))(x−y(22+2i2))\left(x - y\right) \left(x + y\right) \left(x + i y\right) \left(x - i y\right) \left(x - y \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x - y \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x - y \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x - y \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) 
(((((((x + y)*(x - y))*(x + i*y))*(x - i*y))*(x - y*(-sqrt(2)/2 - i*sqrt(2)/2)))*(x - y*(-sqrt(2)/2 + i*sqrt(2)/2)))*(x - y*(sqrt(2)/2 - i*sqrt(2)/2)))*(x - y*(sqrt(2)/2 + i*sqrt(2)/2))
Combinatoria [src] 
                / 2    2\ / 4    4\
(x + y)*(x - y)*\x  + y /*\x  + y /
(x−y)(x+y)(x2+y2)(x4+y4)\left(x - y\right) \left(x + y\right) \left(x^{2} + y^{2}\right) \left(x^{4} + y^{4}\right) 
(x + y)*(x - y)*(x^2 + y^2)*(x^4 + y^4)
Respuesta numérica [src] 
x^8 - y^8
x^8 - y^8
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