Question

Factorize each of the following expression:
x⁸ − 1

Answer 1

$$\begin{gathered} x^8-1 \\ =(x^4{)}^2-1^2 \\ =(x^4-1\left)\right(x^4+1) \\ =[(x^2{)}^2-1^2](x^4+1) \\ =(x^2-1)(x^2+1)(x^4+1) \\ =(x^2-1^2)(x^2+1)(x^4+1) \\ =(x-1)(x+1)(x^2+1)(x^4+1) \end{gathered}$$