Question

factorize 2(x+y)^2 -9(x+y) - 5​

Answer 1

$2 {(x + y)}^{2} - 10(x + y) + (x + y) - 5 \\ 2(x + y)(((x + y) - 5) + 1((x + y) - 5)) \\ (2(x + y) + 1)(x + y - 5)$

Answer 2

Answer : [2(x+y)+1][(x+y)-5]

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Solution :

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Given that : 2(x+y)²-9(x+y)-5 ... (1)

Let, (x+y) = t

Then, from equation (1)

2t²-9t-5

=> 2t²+t-10t-5

=> t(2t+1)-5(2t+1)

=> (2t+1)(t-5)

On putting t = (x+y)

=> [2(x+y)+1][(x+y)-5]