Question

Factorise the following:

x² – 15xy – 54y²

Answer 1

Given expression: x² – 15xy – 54y²

We have to find two numbers whose sum is –15 and the product is –54.

These numbers are –18 and 3.

Now, using the middle term factorisation method.

x² – 15xy – 54y²

= x² – 18xy + 3xy – 54y²

= x(x – 18y) + (3yx – 18y)

= (x – 18y) (x + 3y)

The factorisation result is (x – 18y) (x + 3y).