Question

Factorise the following:

96x² – 216y²

Answer 1

Given expression: 96x² – 216y² 

Step-wise calculation:

Step 1: Take out the common factor.

The greatest common factor (GCF) of 96 and 216 is 24.

So, factor out 24: 96x² – 216y² = 24(4x² – 9y²).

Step 2: Recognize the difference of squares.

4x² – 9y² = (2x)² – (3y)².

Using the identity a² – b² = (a + b)(a – b), factor as (2x + 3y)(2x – 3y).

Step 3: Write the full factorization.

96x² – 216y² = 24(2x + 3y)(2x – 3y).