Question

Factorise the following:

x³ + 64

Answer 1

Given expression: x³ + 64

Step-wise calculation:

1. Recognize that 64 = 4³, so the expression is a sum of cubes:

x³ + 64 = x³ + (4)³

2. Use the sum of cubes factorization formula:

a³ + b³ = (a + b)(a² – ab + b²) where a = x and b = 4

3. Substitute into the formula: (x + 4)(x² – 4x + 16).