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

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Solution

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

Let, $(x + y) = t$ …. (1)

$∴ 2 (x + y)^{2} - 9 (x + y) - 5$

$= 2 t^{2} - 9 t - 5 = 2 t^{2} - 10 t + t - 5$

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

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

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

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

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

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

2 x^{2} + 9 x + 10

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