Question

Factorise the following:

9 – x² + 2xy – y²

Answer 1

Given expression: 9 – x² + 2xy – y²

Step-wise calculation:

1. Rewrite the expression grouping the terms involving x and y:

9 – (x² – 2xy + y²)

2. Recognize that the terms in parentheses form a perfect square:

x² – 2xy + y² = (x – y)²

3. Substitute back:

9 – (x – y)²

4. This is now a difference of squares:

9 – (x – y)² = (3)² – (x – y)²

5. Use the identity a² – b² = (a + b)(a – b):

(3 + (x – y))(3 – (x – y))

6. Simplify the factors:

(3 + x – y)(3 – x + y)