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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

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BenjaminG123
Greetings!

Find the GCF by Grouping.
[tex]mr+ns-nr-ms[/tex]
[tex]mr-ms-nr+ns[/tex]
[tex]m(r-s)-n(r-s)[/tex]
Find the GCF.
[tex](r-s)(m-n)[/tex]
This is the furthest you can factor.

Hope this helps.
-Benjamin

Answer:

(m-n)(r-s)

Step-by-step 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)

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