Question

Factorise the following:

x³ + 8y³

Answer 1

Given: x³ + 8y³

Step-wise calculation:

1. Note that 8y³ = (2y)³, so this is a sum of cubes: x³ + (2y)³.

2. The factorisation formula for a sum of cubes (a³ + b³) is:

a³ + b³ = (a + b)(a² – ab + b²)

Here, a = x and b = 2y. 

3. Applying the formula, we get:

x³ + 8y³ = (x + 2y)(x² – x × 2y + (2y)²) 

x³ + 8y³ = (x + 2y)(x² – 2xy + 4y²)