Question 89 (xiii)

Factorise the following, using the identity, $a^{2} + 2 a b + b^{2} = (a + b)^{2}$

$2 x^{3} + 24 x^{2} + 72 x$

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Solution

We have, $2 x^{3} + 24 x^{2} + 72 x$
$= 2 x (x^{2} + 12 x + 36) = 2 x (x^{2} + 2.6. x + 6^{2})$
$= 2 x (x + 6)^{2} = 2 x (x + 6) (x + 6)$

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Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

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