Question

Factorise the following:

x(2x – y) – y²

Answer 1

Given expression: x(2x – y) – y²

Step-wise calculation:

1. Expand the given expression:

x(2x) – x(y) – y² = 2x² – xy – y²

2. Look for possible factorisation.

The expression is quadratic in terms of x and y: 

2x² – xy – y²

3. Try to factor as (ax + by)(cx + dy).

We want:

ac = 2

bd = –1 

ad + bc = –1

Try a = 2, c = 1 and b = 1, d = –1:

(2x + y)(x – y) = 2x² – 2xy + xy – y²

(2x + y)(x – y) = 2x² – xy – y²

4. Therefore, the factorisation is (2x + y)(x – y).