Question

How do you factor `8m³ - 27n³`?

Answer 1

`(2m-3n)(4m^2+6mn+9n^2)`

Explanation:

Both of these terms are cubed term:

• `8m^3=(2m)^3`
• `27n^3=(3n)^3`

Because of this, this expression is a difference of cubes.

This is a fairly common pattern that can be factored as

`a^3-b^3=(a-b)(a^2+ab+b^2)`

Since `8m^3-27n^3` can be expressed as `(2m)^3-(3n)^3`, we can factor this as if `a=2m` and `b=3n`.

`8m^3-27n^3`

`=(2m)^3-(3n)^3`

`=(2m-3n)((2m)^2+2m(3n)+(3n)^2)`

`=(2m-3n)(4m^2+6mn+9n^2)`