Question

Factorise the following:

`x^4 - 1/x^4`

Answer 1

Given: `x^4 - 1/x^4`

We know that,

(a + b)(a – b) = a² – b²

Hence,

⇒ `(x^2)^2 - (1/x^2)^2`

⇒ `(x^2 + 1/x^2)(x^2 - 1/x^2)`

⇒ `(x^2 + 1/x^2)(x + 1/x)(x - 1/x)`