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

Explanation

Solution
Let `(x + y) =p`, then the expression `2(x + y)²-9(x+y) - 5` becomes `2p² - 9p-5`
Consider the expression `2p²-9p-5` we can factorise it as follows:
`2p²-9p-5=2p² - 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)(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)`