Question

Factorise the following:

x² + y² – 2(xy – xz + yz)

Answer 1

Given expression: x² + y² – 2(xy – xz + yz)

Step-wise calculation:

1. Expand the terms inside the parentheses with the factor –2:

x² + y² – 2xy + 2xz – 2yz

2. Group the terms to see if they can be rearranged or factored:

x² – 2xy + y² + 2xz – 2yz

3. Notice that the first three terms resemble a perfect square:

(x – y)² + 2z(x – y)

4. Factor out the common term (x – y):

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