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

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Solution

Applying the identity: $a^{2} - b^{2} = (a + b) (a - b)$

Using the above identity, the equation $4 x^{2} - 9 y^{2} - 2 x - 3 y$ can be factorised as follows:

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

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

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Factorise :

$4 x^{2} - 9 y^{2}$

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