Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$y^4- 81$
$y^4- 81$
✓
Answer
$ y^4-81 $
$=\left(y^2\right)^2-(9)^2 $
$ =\left(y^2+9\right)\left(y^2-9\right) $
$ =\left(y^2+9\right)\left[(y)^2-(3)^2\right] $
$ =\left(y^2+9\right)(y+3)(y-3) $
$=\left(y^2\right)^2-(9)^2 $
$ =\left(y^2+9\right)\left(y^2-9\right) $
$ =\left(y^2+9\right)\left[(y)^2-(3)^2\right] $
$ =\left(y^2+9\right)(y+3)(y-3) $
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