Question

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

Answer 1

Let $(x+y)=p$, then the expression $2(x+y{)}^2-9(x+y)-5$ becomes $2p^2-9p-5$

Consider the expression $2p^2-9p-5$ we can factorise it as follows:

$2p^2-9p-5=2p^2-10p+p-5=2p(p-5)+1(p-5)=(p-5)(2p+1)$

Now, substitute the value of $p$ as $p=(x+y)$:

$(p-5)(2p+1)=(x+y-5)\left(2\right(x+y)+1)=(x+y-5)(2x+2y+1)$

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