Question

Factorise the following:

7x² + 10xy – 8y²

Answer 1

Given: 7x² + 10xy – 8y²

Step-wise calculation:

1. First, identify two numbers whose product is 7 × (–8) = –56 and whose sum is the middle term coefficient 10.

These numbers are 14 and –4 because 14 × (–4) = –56 and 14 + (–4) = 10.

2. Rewrite the middle term 10xy as 14xy – 4xy:

7x² + 14xy – 4xy – 8y²

3. Group terms:

(7x² + 14xy) – (4xy + 8y²)

4. Factor out common terms from each group:

7x(x + 2y) – 4y(x + 2y)

5. Notice the common binomial factor (x + 2y):

(7x – 4y)(x + 2y)