Question 89 (xiv)

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

$a^{2} x^{3} + 2 a b x^{2} + b^{2} x$

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Solution

We have, $a^{2} x^{3} + 2 a b x^{2} + b^{2} x$
$= x (a^{2} x^{2} + 2 a b x + b^{2}) = x [(a x)^{2} + 2. a x . b + b^{2}]$
$= x (a x + b)^{2} = x (a x + b) (a x + b)$

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

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