Factorize:

2(x + y)² –9(x + y) – 5

We have,

Let x + y = z

Then,

2 (x + y)² – 9 (x + y) - 5

Now by using middle-term splitting, we get

= 2z² - 9z - 5

= 2z² – 10z + z – 5

= 2z (z – 5) + 1 (z – 5)

= (z – 5) (2z + 1)

Now,

Replacing z by (x + y), we get

2 (x + y)² - 9 (x + y) – 5

= [(x + y) – 5] [2 (x + y) + 1]

= (x + y – 5) (2x + 2y + 1)

Hence,

The given expression can be factorized as: