Question

Factorise the following:

4 – (x – y)²

Answer 1

Given: 4 – (x – y)²

Step-wise calculation:

1. Recognize that this is a difference of squares, since 4 = 2² and (x – y)² is already a square.

2. Use the identity a² – b² = (a + b)(a – b) with a = 2 and b = (x – y).

3. So, 4 – (x – y)² = (2)² – (x – y)² 

4 – (x – y)² = (2 + (x – y))(2 – (x – y))

4. Simplify the factors: (2 + x – y)(2 – x + y).