Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$x^4- 1$
$x^4- 1$
✓
Answer
$ x^4-1 $
$ =\left(x^2\right)^2-1 $
$ =\left(x^2+1\right)\left(x^2-1\right) $
$ =\left(x^2+1\right)(x+1)(x-1)$
$ =\left(x^2\right)^2-1 $
$ =\left(x^2+1\right)\left(x^2-1\right) $
$ =\left(x^2+1\right)(x+1)(x-1)$
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