Factorise : $4 a^{2} - 9 b - 2 b c - c^{2}$

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Solution

Given : $4 a^{2} - 9 b - 2 a - 3 b$
We can write it as
$4 a^{2} - 9 b - 2 a - 3 b$ $= (2 a)^{2} - (3 b)^{2} - (2 a + 3 b)$
Based on the equation $a^{2} - b^{2} = (a + b) (a - b)$
We get,
$4 a^{2} - 9 b - 2 a - 3 b$ $= (2 a + 3 b) (2 a - 3 b) - (2 a + 3 b)$
By taking $(2 a + 3 b)$ as common

$4 a^{2} - 9 b - 2 a - 3 b$ $= (2 a + 3 b) (2 a - 3 b - 1)$

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