Question

Factorise the following:

`x^3/8 - y^3`

Answer 1

Given expression: `x^3/8 - y^3`

Step-wise calculation:

1. Recognize the expression as a difference of cubes:

`x^3/8 = (x/2)^3` and y³ = (y)³

2. Use the difference of cubes factorization formula:

a³ – b³ = (a – b)(a² + ab + b²) where `a = x/2` and b = y

3. Substitute into the formula:

`(x/2 - y)((x/2)^2 + x/2 xx y + y^2)`

4. Simplify the terms inside the second bracket:

`(x/2 - y)(x^2/4 + (xy)/2 + y^2)`