Question

Factorise the following:

`64x^3 - 27/y^3`

Answer 1

Given expression: `64x^3 - 27/y^3`

Step-wise calculation:

1. Rewrite each term as a cube:

`64x^3 = (4x)^3`

`27/y^3 = (3/y)^3`

2. The expression becomes a difference of cubes:

`(4x)^3 - (3/y)^3`

3. Use the difference of cubes factorization formula:

a³ – b³ = (a – b)(a² + ab + b²) where a = 4x and `b = 3/y`.

4. Substitute into the formula:

`(4x - 3/y)((4x)^2 + (4x)(3/y) + (3/y)^2)`

5. Simplify inside the second bracket:

`(4x - 3/y)(16x^2 + (12x)/y + 9/y^2)`