Question
Factorise the following, using the identity $a^2- 2ab + b^2= (a - b)^2$.
$a^2y^3- 2aby^2+ b^2y$
$a^2y^3- 2aby^2+ b^2y$
✓
Answer
$ a^2 y^3-2 a b y^2+b^2 y $
$ =y\left(a^2 y^2-2 a b y-b^2\right) $
$ =y\left[(a y)^2-2 \times a y \times b+b^2\right] $
$ =y(a y-b)^2 $
$ =y(a y-b)(a y-b) $
$ =y\left(a^2 y^2-2 a b y-b^2\right) $
$ =y\left[(a y)^2-2 \times a y \times b+b^2\right] $
$ =y(a y-b)^2 $
$ =y(a y-b)(a y-b) $
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