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