Question

Factorise the following:

x² + y² + 2xy – 2x – 2y

Answer 1

Given expression: x² + y² + 2xy – 2x – 2y

Step-wise calculation:

1. Recognize that the first three terms can be grouped into a perfect square: x² + y² + 2xy = (x + y)²

2. Rewrite the expression as: (x + y)² – 2x – 2y

3. Factor out 2 from the last two terms: (x + y)² – 2(x + y)

4. Let p = x + y, then the expression simplifies to: p² – 2p = p(p – 2)

5. Substitute back p = x + y: (x + y)(x + y – 2)