Question
Factorise the following, using the identity $a^2+ 2ab + b^2= (a + b)^2$
$ 4 x^4+12 x^3+9 x^2 $
$ 4 x^4+12 x^3+9 x^2 $
✓
Answer
$ 4 x^4+12 x^3+9 x^2 $
$=x^2\left(4 x^2+12 x+9\right) $
$ =x^2\left[(2 x)+2 \times 2 x \times 3+3^2\right] $
$ =x^2(2 x+3)^2 $
$ =x^2(2 x+3)(2 x+3) $
$=x^2\left(4 x^2+12 x+9\right) $
$ =x^2\left[(2 x)+2 \times 2 x \times 3+3^2\right] $
$ =x^2(2 x+3)^2 $
$ =x^2(2 x+3)(2 x+3) $
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