Factorize each of the following expressions by splitting the middle term: `2(x+y)^2-9(x+y)-5`

Explanation

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 follow:
` 2p^2-9p-5`
=`2p^2-10p+p-5`
=`2p(p-5)+1(p-5)`
=`( p-5)(2p+1)`
Now, substitute of p as `p=(x+y)`:`(p-5)(2p+1)`
=`(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)`