In Exercises 45–68, factor by grouping.ay − by + bx − ax

Question

Accepted Answer

Hello, today we're going to be factoring the given polynomial. So we are given a polynomial of four terms. And whenever you have a polynomial of four terms, we can go ahead and factor this by using factoring by grouping factoring by grouping allows us to group the first two terms together and the last two terms together. And what we want to go ahead and do is factor out a common factor from each of the groups. So in the first group, we have the terms H M minus K M and H M and K M have a common factor of em. So if we factor out M from the first group, what we are left with is M times the quantity H minus K. And in the second group, the terms K N and H N have a common factor of N. So we can go ahead and factor out an end from the second group. And that is going to give us plus N times the quantity K minus H. Now, what we want to do is go ahead and combine these two terms together into a single term. But in order for that to happen H minus K needs to match up with K minus H. So in the second group here, we can go ahead and reorder the terms by switching the negative H and K. So if we just focus on this one group, we have K minus H and switching to two terms is going to give us negative H plus que. Now typically we want to have this first term positive. And in order to make this first term positive, we can go ahead and factor out a negative one from this group. If we factor out a negative one from this group, we get negative H minus K because factoring out a negative one is going to switch the signs of the given terms inside the group. And now if you notice H minus K matches up with H minus K. So just to put this back into the original statement we've written before, we have M times H minus K, but keep in mind that we factor out a negative one. So we have plus negative one times end times the quantity H minus K and negative one times N is going to give us negative N. So we have M times H minus K minus N times H minus K. Now that these two groups match up with each other, we can go ahead and combine this into a single group by combining the leading coefficients together and combining the leading coefficients is going to give us M minus N times the quantity H minus K, which is going to be the factored version of the given polynomial. And with that being said, the answer to this problem is going to be C. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 45–68, factor by grouping.ay − by + bx − ax

Key Concepts

Factoring by Grouping

Common Factors

Binomial Factors

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