Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$ y^4-625 $
$ y^4-625 $
✓
Answer
$ y^4-625 $
$ =\left(y^2\right)^2-(25)^2 $
$ =\left(y^2+25\right)\left(y^2-25\right) $
$ =\left(y^2+25\right)\left(y^2-5^2\right) $
$ =\left(y^2+25\right)(y+5)(y-5) $
$ =\left(y^2\right)^2-(25)^2 $
$ =\left(y^2+25\right)\left(y^2-25\right) $
$ =\left(y^2+25\right)\left(y^2-5^2\right) $
$ =\left(y^2+25\right)(y+5)(y-5) $
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