In Exercises 15–58, find each product. (x+1)(x^2−x+1)

Question

Accepted Answer

Hi there. This problem says to determine the product of the given expression y minus one times two Y squared minus three. So I'm gonna go ahead and write this out first. Why -1 times two Y squared is three. So we're gonna multiply these together which is the product to do that. We're gonna make use of what's called the foil technique. So foil. Since we have our first terms, our outer terms, our inner terms and finally our less terms. So you look at our expression here, the first terms will be the first terms that if you're in each expression right here. So people care why appears first in this first equation to I squared appears first and this other equation we're going to multiply those two together. In other words we have y times two Y squared. Now we'll do the outer terms. So the other terms are just terms on the outside of this entire product expression. So Look here the terms of the outside will be the left most term Y and the right most term -3. So we'll multiply those together. Y plus Y, times negative three. Now we want our inner terms. So the inner terms will be similar to the other terms where we want the terms on the inside of the product expression. So we look here negative one is on the inside and two Y is on the inside. So you want negative one times two went finally we have our last terms. So the last terms are just the last terms in each of our expression. So we have a negative one and negative three. We multiplied those together, ticket negative one times negative three. Now we can go ahead and add all of these together and multiply all these together as well. So by order of operations we first multiply why times two Y squared. That gives us just two Y. To the third By exponent multiplication. No we have Y times negative three. That is just negative three Y. Next we have date of one times two white and this is actually two Y squared. So the one negative one times two I squared. Which in this case is negative two Y squared. Finally we have negative one times negative three. That turns into a plus three. So now we can see if we can combine any like terms in this expression. So the combine like terms we'll look for anything that has the same exponent or power of Y. Or anything like that. So let's see here we have a two Y to the third. It doesn't look like anything is going to add to that. So just bring it down now we go to the next term. I'm actually gonna go to the squared special Next just to keep order of our degrees. So we actually have negative two Y squared. But there's no other thing to multiply or attitude. We're gonna get negative two I square just bring it right down. Now we check our Y. We have negative three Y. There's nothing else to add it to so that we spring it down negative three Y. Finally we have a plus three. Nothing else to add. Just leave it as plus three, meaning our final answer is two. Y cubed minus two Y squared minus three Y plus three. We look at our answers. This is answer D. Alright, I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 15–58, find each product. (x+1)(x^2−x+1)

Key Concepts

Polynomial Multiplication

Distributive Property

Combining Like Terms

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