Question

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

Answer 1

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

Let, $(x+y)=t$ …. (1)

$\therefore 2(x+y{)}^2-9(x+y)-5$

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

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

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

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

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

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