Question 89 (vi)

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

$a^{2} x^{2} + 2 a x + 1$

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Solution

We have, $a^{2} x^{2} + 2 a x + 1$
$= (a x)^{2} + 2. a x .1 + (1)^{2} = (a x + 1)^{2} = (a x + 1) (a x + 1)$

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