Question

How do you factor completely `8x^3 - 18xy^3`?

Answer 1

`8x^3-18xy^3 = 2x(4x^2-9y^3)`

Explanation:

Note that both of the terms are divisible by `2x`, so separate that out as a factor.

`8x^3-18xy^3 = 2x(4x^2-9y^3)`

This is as far as we can go since the degrees of the remaining terms are distinct prime numbers.

If the `y^3` had been `y^2` we would be able to factor the remaining expression as a difference of squares:

`4x^2-9y^2 = (2x)^2-(3y)^2 = (2x-3y)(2x+3y)`

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