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)#