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Factorizar el polinomio x^8-y^8

Expresión a simplificar:

Solución

Ha introducido [src]
 8    8
x  - y 
$$x^{8} - y^{8}$$
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   //
$$\left(x - y\right) \left(x + y\right) \left(x + i y\right) \left(x - i y\right) \left(x - y \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x - y \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x - y \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x - y \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right)$$
(((((((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 /
$$\left(x - y\right) \left(x + y\right) \left(x^{2} + y^{2}\right) \left(x^{4} + y^{4}\right)$$
(x + y)*(x - y)*(x^2 + y^2)*(x^4 + y^4)
Respuesta numérica [src]
x^8 - y^8
x^8 - y^8