Question

Factorise the following:

36x² – 4(y – z)²

Answer 1

Given: 36x² – 4(y – z)²

Step-wise calculation:

1. Note that 36x² = (6x)² and 4(y – z)² = 2(y – z)².

2. We can factor out the common factor 4 from the entire expression:

36x² – 4(y – z)² = 4(9x² – (y – z)²)

3. Inside the parentheses, recognize the expression as a difference of squares:

9x² – (y – z)² = (3x)² – (y – z)²

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

(3x + (y – z))(3x – (y – z))

5. Simplify the terms inside the brackets:

(3x + y – z)(3x – y + z)