How do you factor 8m³ - 27n³?

1 Answer
Jan 23, 2016

(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)