How do you factor #5r ^ { 3} s + 30r ^ { 2} - 5r ^ { 2} s - 30r ^ { 3}#?

2 Answers
Jun 26, 2018

=#5r^2(r-1)(s-6)#

Explanation:

First we notice that #5r^2# is an element in each term, so that
#5r^2s+30r^2-5r^s-30r^3#
=#5r^2(rs+6-s-6r)#
We rearrange:
=#5r^2((rs-6r) -(s-6)#
=#5r^2(r(s-6) -(s-6)#
=#5r^2(r-1)(s-6)#

Jun 26, 2018

#5r^3s+30r^2-5r^2s-30r^3=5r^2(s-6)(r-1)#

Explanation:

#5r^3s+30r^2-5r^2s-30r^3=5r^3s-5r^2s-30r^3+30r^2#
Factoring by grouping, we get
#5r^3s-5r^2s-30r^3+30r^2=5r^2s(r-1)-30r^2(r-1)#
#5r^2s(r-1)-30r^2(r-1)=(5r^2s-30r^2)(r-1)#
Factoring out #5r^2# we get
#(5r^2s-30r^2)(r-1)=5r^2(s-6)(r-1)#
#:.5r^3s+30r^2-5r^2s-30r^3=5r^2(s-6)(r-1)#