Question

Factorise the following:

(3x – 2y)² – 6(3x – 2y) – 135

Answer 1

Given expression: (3x – 2y)² – 6(3x – 2y) – 135

Step-wise calculation:

1. Let p = (3x – 2y). So the expression becomes p² – 6p – 135.

2. We factorise the quadratic expression in p:

Find two numbers whose product is –135 and sum is –6.

Those numbers are –15 and 9, since –15 × 9 = –135 and –15 + 9 = –6.

3. Rewrite the expression: p² – 15p + 9p – 135.

4. Group terms: p(p – 15) + 9(p – 15).

5. Factor out (p – 15): (p – 15)(p + 9).

6. Substitute back p = (3x – 2y): (3x – 2y – 15)(3x – 2y + 9).