Question

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

Answer 1

=`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)`

Answer 2

`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)`