In Exercises 15–58, find each product. (2x−3)^3

Question

Accepted Answer

Hello, today we're gonna be determining the following product of the given expression. So what we are given is eight X minus one cubed. Now eight X minus one cubed is the same thing as saying eight X minus one times itself three different times. So the best way to take this product is to foil together two groups of eight X minus one first, then foil together the remaining groups. So let's go ahead and foil to together together eight X minus one times eight X minus one. In order to foil this group, we're going to take the first term of the first group and distribute it to each term in the second group. So eight X times eight X is going to give us X squared A X multiplied by negative one is going to give us negative eight X. Then we're gonna repeat this process with the second term in the first group and distributed to each term in the second group. So negative one multiplied by eight X is going to give us negative eight X and negative one multiplied by negative one is going to give us positive one. We can go ahead and combine the light terms which are gonna be both of the negative eight X. And we can simplify this to give us 64 X squared minus 16 X plus one. Now keep in mind that this is still being multiplied by a group of eight X minus one. So now what we're going to have to do is we're going to have to foil eight X minus one with the new trinomial we came up with. So just like before we're going to take the first term in the first group, eight X and distribute it to each term in the second group. So eight X times 64 X squared is going to give us 512 X cubed eight X multiplied by negative 16 X is going to give us negative 128 X squared and eight X multiplied by positive one is going to give us positive eight X. Then we continue this process by taking the second term in the first group and distributing it to each term in the second group. So negative one times 64 X squared is going to give us negative 64 X squared. Negative one multiplied by negative 16 X is going to give us positive 16 X and negative one multiplied by positive one is going to give us negative one. So we have this really long polynomial but we can combine like terms together, we can combine negative 128 X squared with negative 64 X squared. And we can combine eight X with 16 X. If we combine the light terms together, we can simplify the polynomial to give us 512 X cubed minus 192 X squared plus 24 X plus minus one. And this is going to be the simplified form of eight X minus one quantity cubed. And with that being said, the answer to this problem is going to be a. 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.

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In Exercises 15–58, find each product. (2x−3)^3

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