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These would be my two factors, excellent work if you got this one correct. You
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might have done this in a couple of ways, let's check out one of the methods. If
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we switch the middle two terms we can see that we'll get a common factor of N in
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the first terms and a common factor by P in the second terms. If we factor a 7 N
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from the first two terms we'll be left with two M and positive one. And if we
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factor a 5p from the second term, we'll be left with 1 and positive 2m. These 2
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factors might appear different but we just wanted to switch the order of these 2
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terms. Remember addition is commutative. Now that we can see there's a common
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factor of 2m plus 1 in the first term and 2m plus 1 in the second term. We
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factor again which leaves us with our factored form, 7n plus 5p times 2m plus 1.
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But we could have regrouped the terms in another way. I could have grouped this
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first term and this last term together and then kept the middle 2 terms together
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as well. If we factor a 2m from these first 2 terms we'll be left with 7n and
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5p. Now in this last group of terms there's only a greatest common factor of 1.
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They don't share any variable factors or number factors. Notice that I have 7n
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plus 5p and 7n plus 5p in these two parenthesis. This is the next common factor.
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So, our two factors are 2m plus 1 and 7n plus 5p. Notice that these answers are
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exactly the same. We've just switched the order of the multiplication. This
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first parenthesis represents a number. And the second parenthesis also
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represents a number. So, it would be like 2 times 3, would be the same as 3
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times 2. Our multiplication is commutative.