In Exercises 15–58, find each product. (x−1)^3

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Hello. Today we're going to be determining the product of a given expression. So the expression given to us is y plus one cubed. Alright so in order to find the product of this we're going to need to expand this quantity while y plus one cubed is like saying you have the quantity Y plus one times itself three times. So you can expand this as Y plus one times Y plus one times Y plus one. And now in order to expand this you're gonna want to foil the quantities together. So that means we're gonna have to foil the 1st and 2nd quantity together. Get that product and then foil the last Y plus one with that product. So let's go ahead and start by foiling Y plus one with Y plus one. So again Y plus one times Y plus one. In order to foil this we're going to take the first term Y and multiply it with Y. And one in the second quantity. Then we're taking a second term one and multiplying it with Y. And one in the second quantity. So y times Y is going to give me Y squared. Why times one is going to give me positive y. One times Y is going to give me positive Y. And one times one It's going to give me one. Now what I want to do is go ahead and combine the like terms here while we can go ahead and combine Y and Y together and that's gonna give us the tri no meal Y squared plus two Y plus one. Alright so that's the product of the first two terms multiplied together. But keep in mind we need to go ahead and multiply this third quantity with this product Y squared plus two Y plus one. So rewriting this we have why plus one times the quantity Y squared plus two Y plus one. Now in order to expand this we're going to need to foil again where we're taking our first term Y and multiplying it with the 1st, 2nd and 3rd term of this trin Amiel. Then we're taking our second term one and repeating the same thing, multiplying to the 1st, 2nd and 3rd term of the binomial. So why times Y squared is going to give me y cubed. Why times two Y is going to give me two Y squared and why times one is just going to give me why now? One times y squared is going to give me y squared one times two Y. Is going to give me two Y and one times one is just going to give me one. Now in order to simplify this we just need to go ahead and combine like terms. While two y squared can be combined with Y squared because of the Y squared term. And y and two Y could be combined together to give us three Y. So we're going to end up with the polynomial Y cubed plus three Y squared plus three Y plus one. And that's going to be the product of Y plus one cubed. That also means that the answer to this problem is going to be is going to be D. So I hope this video helps you in understanding how to find the product of a given expression. And I'll go ahead and see you all in the next video.

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