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Simplificación de expresiones/ Descomposición de multiplicadores/ a^8-1

Factorizar el polinomio a^8-1

Expresión a simplificar:

Solución

Ha introducido [src] 
 8    
a  - 1
a8−1a^{8} - 1 
a^8 - 1
Factorización [src] 
                                /      ___       ___\ /      ___       ___\ /        ___       ___\ /        ___       ___\
                                |    \/ 2    I*\/ 2 | |    \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 |
(a + 1)*(a - 1)*(a + I)*(a - I)*|a + ----- + -------|*|a + ----- - -------|*|a + - ----- + -------|*|a + - ----- - -------|
                                \      2        2   / \      2        2   / \        2        2   / \        2        2   /
(a−1)(a+1)(a+i)(a−i)(a+(22+2i2))(a+(22−2i2))(a+(−22+2i2))(a+(−22−2i2))\left(a - 1\right) \left(a + 1\right) \left(a + i\right) \left(a - i\right) \left(a + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(a + \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(a + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(a + \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) 
(((((((a + 1)*(a - 1))*(a + i))*(a - i))*(a + sqrt(2)/2 + i*sqrt(2)/2))*(a + sqrt(2)/2 - i*sqrt(2)/2))*(a - sqrt(2)/2 + i*sqrt(2)/2))*(a - sqrt(2)/2 - i*sqrt(2)/2)
Respuesta numérica [src] 
-1.0 + a^8
-1.0 + a^8
Combinatoria [src] 
        /     2\ /     4\         
(1 + a)*\1 + a /*\1 + a /*(-1 + a)
(a−1)(a+1)(a2+1)(a4+1)\left(a - 1\right) \left(a + 1\right) \left(a^{2} + 1\right) \left(a^{4} + 1\right) 
(1 + a)*(1 + a^2)*(1 + a^4)*(-1 + a)
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