Question

Factor this expression completely and then place the factors in the proper location on the grid. Note: Place factors alphabetically in the grid! mr + ns - nr - ms

Answer 1

(m-n)(r-s)

Explanation:

We will factor this by grouping. First we rearrange the terms so the m's are together and the n's are together:

mr-ms+ns-nr

Next we group the first two and the last two:

(mr-ms)+(ns-nr)

The GCF of the first group is m; factor this out:

m(r-s)+(ns-nr)

The GCF of the second group is n; factor this out:

m(r-s)+n(s-r)

We want to have the same thing in both sets of parentheses; to do this, we will multiply the second factor by -1:

m(r-s)+-n(r-s)

Factoring out the term now in common, r-s, we have

(r-s)(m-n) = (m-n)(r-s)

Answer 2

Greetings!

Find the GCF by Grouping.

`mr+ns-nr-ms`

`mr-ms-nr+ns`

`m(r-s)-n(r-s)`
Find the GCF.

`(r-s)(m-n)`
This is the furthest you can factor.

Hope this helps.
-Benjamin