Question

Factorise the following:

x² – 2xy + y² – 16

Answer 1

Given: x² – 2xy + y² – 16

Step-wise calculation:

1. Recognize the first three terms as a perfect square trinomial:

x² – 2xy + y² = (x – y)²

2. Rewrite the expression as:

(x – y)² – 16

3. Notice the difference of squares:

(x – y)² – 4² = ((x – y) – 4)((x – y) + 4)

x² – 2xy + y² – 16 = (x – y – 4)(x – y + 4)