# How do you factor #8m³ - 27n³#?

##### 1 Answer

Jan 23, 2016

#### Answer:

#### 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#

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

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

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