Factorise : ${64 a}^{2} + 96 b + {36 b}^{2}$

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Solution

Given expression is $64 a^{2} + 96 b + 36 b^{2}$

The expression can be written as:
$(8 a)^{2} + 2 (8) (6) b + (6 b)^{2}$
We know that, $a^{2} + 2 a b + b^{2} = (a + b)^{2}$
$∴ (8 a)^{2} + 2 (8) (6) b + (6 b)^{2} = (8 a + 6 b)^{2}$
$\Rightarrow (8 a + 6 b) (8 a + 6 b)$ .

Hence, $64 a^{2} + 96 b + 36 b^{2} = (8 a + 6 b) (8 a + 6 b)$ .

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