Question 89 (xvi)

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

$\frac{x^{2}}{4} + 2 x + 4$

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Solution

We have, $\frac{x^{2}}{4} + 2 x + 4$
$= (\frac{x}{2})^{2} + 2. \frac{x}{2} . 2 + 2^{2} = (\frac{x}{2} + 2)^{2} = (\frac{x}{2} + 2) (\frac{x}{2} + 2)$

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