0:00:00.012,0:00:04.337
These would be my two factors, excellent work if you got this one correct. You
0:00:04.337,0:00:08.703
might have done this in a couple of ways, let's check out one of the methods. If
0:00:08.703,0:00:12.798
we switch the middle two terms we can see that we'll get a common factor of N in
0:00:12.798,0:00:16.933
the first terms and a common factor by P in the second terms. If we factor a 7 N
0:00:16.933,0:00:21.546
from the first two terms we'll be left with two M and positive one. And if we
0:00:21.546,0:00:26.142
factor a 5p from the second term, we'll be left with 1 and positive 2m. These 2
0:00:26.142,0:00:30.828
factors might appear different but we just wanted to switch the order of these 2
0:00:30.828,0:00:35.561
terms. Remember addition is commutative. Now that we can see there's a common
0:00:35.561,0:00:39.820
factor of 2m plus 1 in the first term and 2m plus 1 in the second term. We
0:00:39.820,0:00:44.697
factor again which leaves us with our factored form, 7n plus 5p times 2m plus 1.
0:00:44.697,0:00:49.503
But we could have regrouped the terms in another way. I could have grouped this
0:00:49.503,0:00:54.321
first term and this last term together and then kept the middle 2 terms together
0:00:54.321,0:00:58.912
as well. If we factor a 2m from these first 2 terms we'll be left with 7n and
0:00:58.912,0:01:04.001
5p. Now in this last group of terms there's only a greatest common factor of 1.
0:01:04.001,0:01:09.429
They don't share any variable factors or number factors. Notice that I have 7n
0:01:09.429,0:01:14.966
plus 5p and 7n plus 5p in these two parenthesis. This is the next common factor.
0:01:14.966,0:01:20.042
So, our two factors are 2m plus 1 and 7n plus 5p. Notice that these answers are
0:01:20.042,0:01:24.159
exactly the same. We've just switched the order of the multiplication. This
0:01:24.159,0:01:28.025
first parenthesis represents a number. And the second parenthesis also
0:01:28.025,0:01:31.992
represents a number. So, it would be like 2 times 3, would be the same as 3
0:01:31.992,0:01:34.453
times 2. Our multiplication is commutative.