Question

Factorise by substituting terms:

(2x – y)² – 14x + 7y – 18

Answer 1

Given expression: (2x – y)² – 14x + 7y – 18

= (2x – y)² – 7(2x – y) – 18

We have to find two numbers whose sum is –7 and the product is –18. 

These numbers are –9 and 2.

Now, using middle term factorisation method,

(2x – y)² – 7(2x – y) – 18

= (2x – y)² – 9(2x – y) + 2(2x – y) – 18

= (2x – y) [(2x – y) – 9] + 2[(2x – y) – 9]

= [(2x – y) – 9] [(2x – y) + 2]

= (2x – y – 9) (2x – y + 2)

The factorisation result is (2x – y – 9) (2x – y + 2).