Question
Factorise the following, using the identity $a^2+ 2ab + b^2= (a + b)^2$
$2x^3+ 24x^2+ 72x$
$2x^3+ 24x^2+ 72x$
✓
Answer
$ 2 x^3+24 x^2+72 x $
$ =2 x\left(x^2+12 x+36\right) $
$ =2 x\left(x^2+2 \times 6 \times x+6^2\right) $
$ =2 x(x+6)^2 $
$ =2 x(x+6)(x+6) $
$ =2 x\left(x^2+12 x+36\right) $
$ =2 x\left(x^2+2 \times 6 \times x+6^2\right) $
$ =2 x(x+6)^2 $
$ =2 x(x+6)(x+6) $
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