Question

Factorise the following:

9x² – 4(x + y)²

Answer 1

Given expression: 9x² – 4(x + y)²

Step-wise calculation:

1. Recognize the expression as a difference of two squares:

9x² – 4(x + y)² = (3x)² – [2(x + y)]²]

2. Apply the difference of squares formula a² – b² = (a + b)(a – b): 

(3x + 2(x + y))(3x – 2(x + y))

3. Expand inside the parentheses:

(3x + 2x + 2y)(3x – 2x – 2y)

4. Simplify each parenthesis:

(5x + 2y)(x – 2y)