Factorize:$9(2a - b)^2 - 4(2a - b) - 13$

Given :

To do :

We have to factorize the given expression.

Solution :

$9(2 a-b)^{2}-4(2 a-b)-13$

Let $2 a-b=x$

This implies,

$9(2 a-b)^{2}-4(2 a-b)-13=9 x^{2}-4 x-13$

$=9 x^{2}+9 x-13 x-13$

$=9 x(x+1)-13(x+1)$

$=(x+1)(9 x-13)$

$\Rightarrow 9(2 a-b)^{2}-4(2 a-b)-13=(2 a-b+1)[9(2 a-b)-13]$

$=(2 a-b+1)(18 a-9 b-13)$

Hence, $9(2 a-b)^{2}-4(2 a-b)-13=(2 a-b+1)(18 a-9 b-13)$.

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Updated on: 10-Oct-2022

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