Factorize:$2(x+y)^2 - 9(x+y) -5$

Given :

To do :

We have to factorize the given expression.

Solution :

$2(x+y)^2 - 9(x+y) -5$

Let $x+y=a$

This implies,
$2(x+y)^2 - 9(x+y) -5=2 a^{2}-9 a-5$

$=2 a^{2}-10 a+a-5$

$=2 a(a-5)+1(a-5)$

$=(a-5)(2 a+1)$

Therefore,

$2(x+y)^2 - 9(x+y) -5=(x+y-5)[2(x+y)+1]$

$=(x+y-5)(2x+2y+1)$

Hence, $2(x+y)^2 - 9(x+y) -5=(x+y-5)(2x+2y+1)$.

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Updated on: 10-Oct-2022

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