Solve: x^8-1 - Vidyadip

Question

Solve:
$ x^8-1$

✓

Answer

$ x^8-1=\left(x^4\right)^2-1^2 $
$ =\left(x^4-1\right)\left(x^4+1\right) $
$ =\left[\left(x^2\right)^2-1^2\right]\left(x^4+1\right) $
$ =\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right) $
$ =\left(x^2-1^2\right)\left(x^2+1\right)\left(x^4+1\right) $
$ =(x-1)(x+1)\left(x^2+1\right)\left(x^4+1\right) $

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