Factorise:
$36 a^{2} + 12 a b c - 15 b^{2} c^{2}$

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Solution

$36 a^{2} + 12 a b c - 15 b^{2} c^{2}$

$= 3 (12 a^{2} + 4 a b c - 5 b^{2} c^{2})$

$= 3 (12 a^{2} + 10 a b c - 6 a b c - 5 b^{2} c^{2})$

$= 3 (2 a (6 a + 5 b c) - b c (6 a - 5 b c))$

$= 3 (2 a - b c) (6 a + 5 b c)$

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