Question

Factorise the following:

x³ – 8

Answer 1

Given expression: x³ – 8

Step-wise calculation:

1. Recognize that this is a difference of cubes.

We can write: x³ – 8 = x³ – 2³

2. Use the identity for the difference of cubes:

a³ – b³ = (a – b)(a² + ab + b²)

3. Substitute a = x and b = 2: 

x³ – 2³ = (x – 2)(x² + 2x + 2²) which simplifies to (x – 2)(x² + 2x + 4).