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

Factorizar el polinomio b^8-c^8

Expresión a simplificar:

Solución

Ha introducido [src] 
 8    8
b  - c
b8−c8b^{8} - c^{8} 
b^8 - c^8
Factorización [src] 
                                    /      /    ___       ___\\ /      /    ___       ___\\ /      /  ___       ___\\ /      /  ___       ___\\
                                    |      |  \/ 2    I*\/ 2 || |      |  \/ 2    I*\/ 2 || |      |\/ 2    I*\/ 2 || |      |\/ 2    I*\/ 2 ||
(b + c)*(b - c)*(b + I*c)*(b - I*c)*|b - c*|- ----- - -------||*|b - c*|- ----- + -------||*|b - c*|----- - -------||*|b - c*|----- + -------||
                                    \      \    2        2   // \      \    2        2   // \      \  2        2   // \      \  2        2   //
(b−c)(b+c)(b+ic)(b−ic)(b−c(−22−2i2))(b−c(−22+2i2))(b−c(22−2i2))(b−c(22+2i2))\left(b - c\right) \left(b + c\right) \left(b + i c\right) \left(b - i c\right) \left(b - c \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(b - c \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(b - c \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(b - c \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) 
(((((((b + c)*(b - c))*(b + i*c))*(b - i*c))*(b - c*(-sqrt(2)/2 - i*sqrt(2)/2)))*(b - c*(-sqrt(2)/2 + i*sqrt(2)/2)))*(b - c*(sqrt(2)/2 - i*sqrt(2)/2)))*(b - c*(sqrt(2)/2 + i*sqrt(2)/2))
Respuesta numérica [src] 
b^8 - c^8
b^8 - c^8
Combinatoria [src] 
                / 2    2\ / 4    4\
(b + c)*(b - c)*\b  + c /*\b  + c /
(b−c)(b+c)(b2+c2)(b4+c4)\left(b - c\right) \left(b + c\right) \left(b^{2} + c^{2}\right) \left(b^{4} + c^{4}\right) 
(b + c)*(b - c)*(b^2 + c^2)*(b^4 + c^4)
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