Question

How do you factor `32x^3-500y^3`?

Answer 1

`4(2x - 5y)(4x^2 + 10xy + 25y^2)`

Explanation:

First extract common factors
`(32x^3 - 500 y^3) = 4(8x^3 - 125y^3)`
The term in brackets is now the difference of cubes, which can be factored as `a^3 – b^3 = (a – b)(a^2 + ab + b^2)`
So
`32x^3 - 500y^3 = 4(2x - 5y)(4x^2 + 10xy + 25y^2)`