Question

Factorise the following:

27x³ + 8

Answer 1

Given: 27x³ + 8

Step-wise calculation:

This expression is a sum of two cubes since:

27x³ = (3x)³ and 8 = 2³ 

The formula for factorising a sum of cubes (a³ + b³) is:

a³ + b³ = (a + b)(a² – ab + b²) 

Using a = 3x and b = 2, we get:

27x³ + 8 = (3x + 2) ((3x)² – (3x)(2) + 2²) 

Simplify inside the bracket:

(3x + 2)(9x² – 6x + 4)