In Exercises 15–58, find each product. (2x−5)(7x+2)

Question

Accepted Answer

Hi there. This problem says, determine the product by the given expression two x minus one times X plus two. So I'm gonna rewrite this first. We have two X minus one times X plus two. So when you multiply these together, that's what the product means. So I'm gonna make use of what's called the foil technique. The foil technique says that we have our first terms, our outer terms, our inner and our last terms. So explain this. If we work at our two expressions here, we're talking about our first terms first. So the first term is for each expression we have here is the very first term or thing that appears in the expression. So in our case our two X. The first thing appears in this one and our X. The first thing appears and the other one. So get them multiply those together two x times x. Now we want the outer terms. So the other terms are the terms on the outside of this product expression. So if you look here to excess to the left most side and two is to the right most side. So we're gonna multiply those together two X Times two. Now we want our inner terms. So the inner terms. Some of the other terms are terms that are on the inside of the project expression. So if you look here are negative, one is inside and our X is inside as well. So we're gonna multiply those two together. Just one times X. Finally our last terms are the last terms in both of our expressions. So if you look here, we have a negative one at the end and a two at the end of each expression. So We do -1 times two. Now that we have our foil taken care of. We're gonna multiply all these together and simplify. So you have two X times X. You have two X squared. Now we have two X times two that is or X. Next we have negative one times X. That is just negative X. And finally negative one times two. That is just negative two. So now that we're here we can go ahead and combine like terms to simplify. So if you look at our terms here the light terms will just be anything that has the same expiry or power or anything like that. We're gonna combine those together. So people care two X squared. There's no other X squared in this expression. So that's just going to come drag me down to a square. Now look here we have a four X. And a negative X. Those have the same power of X. So we can combine these we have four x minus one X. That is plus three X. Finally we don't have any more expressions that combined with the two. So you bring down the negative to the answer to our problem is two X squared plus three x minus two which in this case is answer be okay I hope to help you solve the problem. Thank you for watching. Goodbye

In Exercises 15–58, find each product. (2x−5)(7x+2)

Key Concepts

Distributive Property

Binomial Multiplication

Combining Like Terms

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