Factorise: $36 c^{2} - (5 a + b)^{2}$

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Solution

We have:
$36 c^{2} - (5 a + b)^{2}$
$= (6 c)^{2} - (5 a + b)^{2}$
$= (6 c + 5 a + b) [6 c - (5 a + b)]$ [ $∵ (a^{2} - b^{2}) = (a + b) (a - b)$ ]
$= (6 c + 5 a + b) (6 c - 5 a - b)$
$∴ 36 c^{2} - (5 a + b)^{2} = (6 c + 5 a + b) (6 c - 5 a - b)$

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