In Exercises 15–58, find each product. (4x^2−1)^2

Question

Accepted Answer

Hi there. This problem says to determine the product at the given expression X squared minus nine squared. So solve this problem. We're gonna make use of the foil technique. So but first before I do that I will first go ahead and split up our expression. So we have x squared minus nine squared. That just means we have x squared minus nine times X squared minus nine. Now you can look at the foil technique. So foil tells us that if we are multiplying two polynomial together in this case we have to square polynomial Only two terms each. We're going to multiply in a specific order. We have the first terms which are the very first terms for each polynomial. We have our outer terms. So I'll make this with the red outer which are the first term of this one and the last term of this one. We have the inner where we have our inner two terms. So innermost terms. And we have our list where last terms are the very last two terms in our polynomial. So I'll make lines between these. We have our first we have our outer we have our inner and we have our list. Let's go ahead and multiply all these together. So our first terms we have x squared times X script. Now the other terms we have an X squared and a negative none. Our inner terms. We have an X squared and another negative none. And finally our last terms we have a negative nine and a negative night multiply all of those together and then we add the different parts. So let's take X squared times X squared. Well X squared times X squared by exponents multiplication. This is X to the 4th. Now we have a negative nine times X square. That gives us negative nine X squared. Same thing over here, negative nine times X squared is nine X squared. Finally negative nine times negative nine gives us a positive 81. No I can simplify even further. We have excellent forts. Now we have our negative nine X squared minus and nine X squared. Since we can combine like terms this turns into a -18 x square. And finally we just bring down our plus 81. So we have reached the end of our simplification meaning that our answer is X to the fourth minus 18 X squared plus 81. Which in this thing is answer A. Okay I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 15–58, find each product. (4x^2−1)^2

Key Concepts

Binomial Expansion

Square of a Binomial

Polynomial Multiplication

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