In Exercises 15–58, find each product. (7x^2−2)(3x^2−5)

Question

Accepted Answer

Hi there. This problem says determine the product of the given expression. Four X squared plus six times X squared plus one. I'm gonna go ahead and rewrite this first. So you have four X squared plus six times X squared plus one. So to solve this, I'm gonna make use of what's called the foil technique. So foil says we have our first terms, our outer terms, our inner and our last So filter needs to say that we're going to multiply these numbers together. So if you look at our two expressions here, the first terms are given by our four X squared and R X squared. They are the first terms that appear in each of our expressions. So we have four X squared and X squared square times square. Now we look at our outer terms to the other terms are the outer two terms as a whole of both of our expressions. So if you look at this, the terms on the outside will be the four X squared as on the left most side and the one which is on the right most side. So I'll go ahead and add for it squared times 20. Now we want our inner terms. So the inner terms similar to the other terms are the terms that are inside the entire product expression. So if you look here we have R six and R X square. These terms are inside so we do plus six times X square. Finally we will get our last terms. So the last terms are the last terms in each of our expressions. In other words we have R. Six and R. One. These are the last terms in both expressions So we add six times one. Now we can go ahead and multiply everything together. So we have four X squared times X squared by exponent multiplication. This is four X to the fourth. Now we have four square times one, that's just four x squared. Now we have six times X squared. That is six X square. Finally we have six times one which is just six. Now that we're here we can go ahead and combine any like terms that we have. So like term is just any term that has the same exponents or power or anything like that. So if you notice here our four X squared and six X squared have the same exponent X squared. So I'm going to bring down this four X to the fourth because it doesn't have anything to combine. Then we look at our four X squared plus six X squared four X squared plus six X squared is just 10 X square. Finally we bring down our positive six since there's no other terms to combine with that. Plus six meaning that our answer is four X to the fourth plus 10 X squared plus six which is answer a thanks for watching. I hope to help you solve the problem. Goodbye

In Exercises 15–58, find each product. (7x^2−2)(3x^2−5)

Key Concepts

Polynomial Multiplication

Distributive Property

Combining Like Terms

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