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Simplificación de expresiones/ Descomposición de multiplicadores/ a^8-b^8

Factorizar el polinomio a^8-b^8

Expresión a simplificar:

Solución

Ha introducido [src] 
 8    8
a  - b
a8−b8a^{8} - b^{8} 
a^8 - b^8
Factorización [src] 
                                    /      /    ___       ___\\ /      /    ___       ___\\ /      /  ___       ___\\ /      /  ___       ___\\
                                    |      |  \/ 2    I*\/ 2 || |      |  \/ 2    I*\/ 2 || |      |\/ 2    I*\/ 2 || |      |\/ 2    I*\/ 2 ||
(a + b)*(a - b)*(a + I*b)*(a - I*b)*|a - b*|- ----- - -------||*|a - b*|- ----- + -------||*|a - b*|----- - -------||*|a - b*|----- + -------||
                                    \      \    2        2   // \      \    2        2   // \      \  2        2   // \      \  2        2   //
(a−b)(a+b)(a+ib)(a−ib)(a−b(−22−2i2))(a−b(−22+2i2))(a−b(22−2i2))(a−b(22+2i2))\left(a - b\right) \left(a + b\right) \left(a + i b\right) \left(a - i b\right) \left(a - b \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(a - b \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(a - b \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(a - b \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) 
(((((((a + b)*(a - b))*(a + i*b))*(a - i*b))*(a - b*(-sqrt(2)/2 - i*sqrt(2)/2)))*(a - b*(-sqrt(2)/2 + i*sqrt(2)/2)))*(a - b*(sqrt(2)/2 - i*sqrt(2)/2)))*(a - b*(sqrt(2)/2 + i*sqrt(2)/2))
Combinatoria [src] 
                / 2    2\ / 4    4\
(a + b)*(a - b)*\a  + b /*\a  + b /
(a−b)(a+b)(a2+b2)(a4+b4)\left(a - b\right) \left(a + b\right) \left(a^{2} + b^{2}\right) \left(a^{4} + b^{4}\right) 
(a + b)*(a - b)*(a^2 + b^2)*(a^4 + b^4)
Respuesta numérica [src] 
a^8 - b^8
a^8 - b^8
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