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

Question

Accepted Answer

Hi. So this problem has to determine the product of the given expression. Two x minus three squared. So the product means we're gonna multiply this together. So we have two things we're going to supply. You have two X -3. Since it's squared. We're multiplying it by itself two X -3. So you want to simplify this multiplication to do this. We're going to make use of what's called the foil technique. So the foil technique says that we multiply our first terms together, our outer terms together our inner terms and our last terms and add everything together at the end. So let's look at our falsification here. Oil, we'll start with first terms. So the first terms are the very first terms in each of our polynomial or in this case they're just linear expressions. So the first term of this one is two x. And on the other one is also two X. So our first is two X times two X. Now it went the outer terms. The other terms in this case are the terms that are on the utmost side of this set of expressions. So what I mean by that is two X is on the utmost side to the left. Now you have three is on the utmost side to the right. So multiply our two X and our negative three. So you have plus two X times negative three. Now we'll do our inner terms similar to outer. The inner is just our innermost two terms. In this case we have negative three Times are positive two x. So -3 times two x. Finally our last terms are the last two terms in each of our expressions. So in this case -3 is the last term for this one and also last term for the second one. So you have native three times negative three. So now we can go ahead and simplify all of our multiplication. We have two X times two X. Which is four X squared. You have negative three times two X. Which is negative six X. Another negative three times two X. Which is once again negative six X. And finally negative three times negative three which is positive. Not now. We're almost there now we can go ahead and simplify our like terms. So we combine our like terms here. The only two like terms we have are the six X. Is because they both are just X. So I'll bring down like four X squared. We have native six X minus six X. Gives us native 12 X. And we can also bring down our nuts. That doesn't have any more terms plus nine. Now we have no more simplification left to do which means our answer is just four X squared minus 12 X. Plus nine which means we have answer. D Okay I hope to help you solve the problem. Thank you for watching. Goodbye

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

Key Concepts

Binomial Expansion

Algebraic Manipulation

Quadratic Expressions

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