00:01
This problem wants us to simplify the rational expression we see, and what we have in our numerator and denominator are four term polynomials.
00:09
And the only way we can factor four term polynomials to try to simplify this is by grouping.
00:15
And to group what we're going to do is put our terms that have like things together and rearrange this a little bit.
00:21
So when i'm trying to factor our numerator, i'm going to put 2xy -2y and then plus 5x -5 to rearrange the order so i have my y terms to the left and non -y terms to the right.
00:35
And now the first step of factoring by grouping is to group our first two terms and our last two terms.
00:41
And then we look for a gcf or a common factor from both binomials individually.
00:47
So 2xy -2y has a factor gcf of 2y, and when we factor that out that leaves us with x -1.
00:54
From our second binomial 5x -5 we can factor out a positive 5, and that also leaves us with x -1.
01:01
So when you're factoring by grouping and the result binomial that's left over matches, that means you're doing it correctly.
01:08
And the way to finish your factoring is by grouping your gcfs together in one binomial.
01:14
So that would be 2y -5, and then we write our shared binomial only once instead of twice even though you see it two times...