Factorise: $4 (a + b)^{2} - 9 (a - b)^{2}$

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Solution

Given expression is $4 (a + b)^{2} - 9 (a - b)^{2}$
By using identity $a^{2} - b^{2} = (a + b) (a - b)$
It can be factorised as $4 (a + b)^{2} - 9 (a - b)^{2} = [(2 (a + b))^{2} - (3 (a - b))^{2}]$
$= [2 (a + b) + 3 (a - b)] [2 (a + b) - 3 (a - b)]$
$= [2 a + 2 b + 3 a - 3 b] [2 a + 2 b - 3 a + 3 b]$
$= (5 a - b) (5 b - a)$
Thus factors are $5 a - b, 5 b - a$ .

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