# How do you factor #14r^4-378rs^3#?

##### 1 Answer

May 9, 2016

#### Explanation:

First note that both terms are divisible by

#14r^4-378rs^3 = 14r(r^3-27s^3)#

Next note that both

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

with

#r^3-27s^3#

#=r^3-(3s)^3#

#=(r-3s)(r^2+r(3s)+(3s)^2)#

#=(r-3s)(r^2-3rs+9s^2)#

Putting it all together:

#14r^4-378rs^3 = 14r(r-3s)(r^2+3rs+9s^2)#