Factorise : $4 x^{2} - 9 y^{2} - 2 x - 3 y$

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Solution

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

$4 x^{2} - 9 y^{2} - 2 x - 3 y$ $= (2 x + 3 y) (2 x - 3 y - 1)$

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