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.

(2x−3)(4x−5)

Accepted Answer

Hey, everyone. Welcome back 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? The first binomial we're given is 2 D -5. And that's multiplied by the second binomial 0D -9. We're given four answer choices. Option A six D squared plus 3d minus 45. Option B six D squared plus 30 3d plus 45. Option C six D squared minus 3d minus 45 in option D six D squared minus 30 3d plus 100 or sorry plus 45. Now, the first thing we're gonna do is rewrite the binomials. We've been given two D minus five is the first binomial and that's multiplied by 3d minus nine. The second binomial, we're asked to use the foil method of multiplication and the foil method represents first outside inside last. So we want to take the first terms of our expression multiply them together. Take the outside terms of our binomials, multiply them together. Take the inside terms of our binomial multiply them together and then take the last terms of our binomial and multiply them together And if we add these four terms, we are gonna get our resulting expression for the multiplication. So let's go ahead and do that starting with the first terms. So the first term of the first binomial is 2D the first term of the second binomial is 3d. So we get two D multiplied by 3d. And this represents our first terms. Then we add next, we have the outside terms. So we're gonna take the terms on the outermost of our expression. So the far left and the far right, on the far left from the first binomial, we have two D on the far right from the second binomial, we have negative nine. So we have two D multiplied by -9. This represents our outside terms or the Owen foil. Then we add next, we're gonna take the inside terms. So those innermost terms that are closest together from each final meal. So on the inside, from binomial one, we have negative five and from binomial two, we have 3d. So we get negative five multiplied by 0D. This represents our inside terms or the eye and foil one more time for our final term. This term is gonna be the last terms. So we're gonna take the last term from our first binomial. The last term from our second binomial and multiply them together. We have negative 5 and -9. So we have negative five multiplied by -9. This represents the last terms or the L in foil. Now, we've applied the foil method. We've done the multiplication. And what's left to do is just to simplify this expression, starting with our first terms, we had two D multiplied by 3d. OK. So the coefficient two multiplied by three is going to give us a coefficient of six. And then we have d multiplied by D recall when you multiply two things together with the same base, the exponents add. So we get D to the exponent one plus one, we have two D multiplied by negative nine. This is gonna give us negative 18 D, our next term negative five multiplied by 0D. This gives us negative 15 d and finally negative five multiplied by -9 gives us positive 45. So we add that to our expression. OK. So we've simplified quite a bit. We have a little bit more, one more step we can do. So let's do that. In this first term, we can simplify the exponent we have six D to the exponent one plus one. We can write this as six D squared. We have negative 18 d -15 d and we can simplify this and write it as minus 30 3d and we have plus 45 that constant term that can't be simplified any further. And that's it. Here is our resulting expression. We have ad squared term ad squared and a constant term. And we can't simplify further comparing this to our answer choices. OK. We found using the foil method of multiplication. The product of the binomials we were given is six D squared minus 30 3d plus 45 which corresponds with answer choice. D 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. (2x−3)(4x−5)

Key Concepts

FOIL Method

Binomials

Distributive Property

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