Question

Factorise the following:

125x³ – 64

Answer 1

Given: 125x³ – 64

Step-wise calculation:

1. Recognize that 125x³ is a cube since 125 = 5³ and x³.

Also, 64 = 4³. 

Thus, 125x³ – 64 = (5x)³ – 4³.

2. Use the difference of cubes formula:

a³ – b³ = (a – b)(a² + ab + b²) 

Here, a = 5x and b = 4.

3. Apply the formula:

(5x – 4)((5x)² + (5x)(4) + 4²) 

= (5x – 4)(25x² + 20x + 16)