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