Question

Factorise the following:

`x^8 - 1/x^8`

Answer 1

Given `x^8 - 1/x^8`

We know that,

(a + b) (a – b) = a² – b²

Hence,

⇒ `(x^4)^2 - (1/x^4)^2`

⇒ `(x^4 + 1/x^4) (x^4 - 1/x^4)`

⇒ `(x^4 + 1/x^4) (x^2 + 1/x^2) (x^2 - 1/x^2)`

⇒ `(x^4 + 1/x^4) (x^2 + 1/x^2) (x - 1/x) (x + 1/x)`