Question

Factorise by substituting terms:

5(x + y)² – 6x – 6y – 8

Answer 1

Given expression: 5(x + y)² – 6x – 6y – 8

= 5(x + y)² – 6(x + y) – 8

We have to find two numbers whose sum is –6 and whose product is –40. 

These numbers are –10 and 4.

Now, using middle term factorisation method,

5(x + y)² – 6(x + y) – 8

 = 5(x + y)² – 10(x + y) + 4(x+ y) – 8

= 5(x + y) [(x + y) – 2] + 4[(x + y) – 2]

= [(x + y) – 2] [5(x + y) + 4]

= (x + y – 2) (5x + 5y + 4)

The factorisation result is (x + y – 2) (5x + 5y + 4).