In Exercises 35–54, use the FOIL method to multiply the binomials...

Question

In Exercises 35–54, use the FOIL method to multiply the binomials.

(x−4)(x²−5)

Accepted Answer

Hey, everyone in this video, we're gonna work through the following problem using the foil method of multiplication. What is the product of the following binomials? We're given the binomial V -2, multiplied by the binomial V squared minus six. We have four answer choices. Option A V cubed minus two V squared minus six V plus 12. Option B V cubed minus two V squared plus six V plus 12. Option CV cubed minus two V squared plus six V minus 12. Then option D V cubed minus two V squared minus six V minus 12. Gonna start by rewriting the expression we were given V -2, multiplied by V squared minus six are two binomials. And we're asked to use the foil method and recall that the foil method tells us to take the first terms and multiply them together. Take the outside terms, multiply them together, take the inside terms multiply them together, then take the last terms and multiply them together. And we're gonna take these four results, add them up and that's gonna give us the resulting expression of our multiplication. So let's go ahead and do that. So if we take the first term from each binomial. From the first binomial, we have B in the second binomial, we have B squared. So we get V multiplied by V squared and then we're gonna add, OK. And this V multiplied by V squared represents our first terms or the F in foil. And we're gonna add now the outside terms. So we're gonna take the outermost terms, the term on the far left, the term on the far right from our first binomial, the term on the far left is V from our second binomial. The term on the far right is -6. And so we have V multiplied by -6. And this represents our outside terms or the O in foil, then we're going to add and we're gonna add the inside terms. OK? So the ones that are closest together in the middle. So from our first binomial, we have negative two, from our 2nd final meal, we have V squared. So we get negative two multiplied by V squared for our inside terms, the eye and foil. Then finally, we're gonna add and this time we're gonna add the last terms. So we're gonna take the last term of the first binomial, which is -2. We're gonna multiply by the last term of the second binomial negative six, -2 multiplied by -6. And this represents our last terms or the L in foil. So now we've used the foil method, we've done the multiplication and what's left to do is to simplify this extraction. Starting with our first term, we have V multiplied by V squared. Recall when you multiply something with the same base, we're gonna add the exponents. This is gonna become V to the exponent one plus two. Our next term we have nega or V multiplied by negative six and this gives us -6 v. So we're gonna subtract six V in our expression. Our next term negative two multiplied by V squared. We get negative two V squared and subtracting two V squared in our last term, negative two multiplied by negative six gives us positive 12. So we have plus 12. At the end, we can simplify this a little further. We're also gonna rearrange in our answer choices. The expression goes in descending order of the exponent. So it has the V cube term, then the V squared term, then the V term then the constant term. So we're gonna rewrite our expression to be in that same format so that it's easier to compare to the answer choices. So starting with our V cube term, we have V to the exponent one plus two, we can simplify this to be V cubed. Then we want to write our V squared term which is negative to V squared. And we want to write our V term negative six V in our constant term bless. Now this is as simplified as we can get this expression. And So this is the result we were looking for if we compare this to our answer choices, OK. We found using the foil method of multiplication. The product of the binomials we were given is V cubed minus two V squared minus six V plus 12, which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 35–54, use the FOIL method to multiply the binomials. (x−4)(x²−5)

Key Concepts

Binomials

FOIL Method

Polynomial Multiplication

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