![]() Us to say what pattern can we use to factor the expression. And if this is equal to V squared, well, that means that V isĮqual to Y plus three. Squared then that means that capital U is equal to six X squared. Times U minus V is equal to U squared minus V squared. So this is making me feel pretty good about this pattern but They both look like they are the square of something and we haveĪ difference of squares. So the same idea, they wanna factor the following expression. Pause the video and see if you can work this one out on your own. If I were to multiply this out, this is going to be equal to, this is a difference of squaresĪnd we've seen this before. U V would be equal to, well, you're not gonna have any Y in it so this is not going to be two U V. Now is this equal to two times U V? Well, let's see, two times And if this is V squared then that means that V is equal to five. U is going to be equal to two X to the third power. If this is U squared, if this is U squared then that means that It looks like maybe I could use, I can see a perfect square here. What pattern can we use to factor the expression? So I have these three terms here. We're given a different expression and they're asking us So I would go with thatĬhoice right over there. Well, I would use a pattern for U plus V squared. So when they say which pattern can we use to factor this expression, So notice this polynomial,Įxpressed in this pattern, which means it can be factored this way. U times V I get three X to the fourth Y and then two times that is indeed six X to the fourth Y. Is capital V squared then that means that V is equal to Y. And if we said that V squared is equal to Y squared, so if this 'Cause notice if you square this you're gonna get nine X to the eighth. How can it have this form? Well, if we view U squared as nine X to the eighth then that means that U is, and let me write it as a capital U, U is equal to three X to the fourth. This polynomial right over here, it actually has this form if you look at it carefully. This is going to be equal to U squared plus two times the product of these terms so two U V and then plus V squared. That pattern to factor "it into one of these forms?" What do I mean by that? Well, let's just imagine something like U plus V squared. So when they're talking about patterns they're really saying, "Hey, can we say "that some of these can generally form "a pattern that matches what we have here "and then we can use So we'll do this one together and then we'll have a few more examples where I'll encourage you to pause the video. To factor the expression? And U and V are either constant integers or single-variable expressions. ![]() Told that we wanna factor the following expression and they ask us which pattern can we use
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