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.(3y−4)(2y−1)

Accepted Answer

Hey, everyone in this video, we're gonna be working through the following problem using the foil method of multiplication. What is the product of the following binomials? The binomials were given. We have the first one is 5K -3 and that's multiplied by the second binomial 4 K -1. We have four answer choices. Option A negative 12 K squared plus 23 K plus five. Option B negative 12 K squared plus 23 K minus five. Option C 20 K squared minus K plus three in option D 20 K squared minus 17 K minus three. We're gonna start by rewriting what we've been given. So we're gonna rewrite the binomials. We have five K minus three, multiplied by the 2nd Binomial 4 K -1. Now, we're asked to use the foil method and foil recall stands for first outside, inside and last. So we want to take the first terms of our binomials multiply them together. Take the outside terms of our binomial multiply them together, take the inside terms, multiply them together and finally the last terms and multiply them together. This is gonna give us four terms. We add those all together to get a resulting expression from that multiplication. So let's get started on the foil method starting with the first terms. The first term of the first binomial is 5K. The first term of the second binomial is 4K. So we have 5K multiplied K. And again, this represents our first terms or the F in foil. Now we move to the outside terms. So we want the terms on the outside of our expression. So the leftmost term and the right most term from the first binomial, we have the utmost term is 5K from the second binomial. The odor term is -1. We're gonna add five K multiplied by -1. And again, this represents our outside terms, the O and foil moving to the inner terms. So we did the outside terms. Now we wanna do the inside terms. So we want those inner terms that are closest together between the two by no means. And we're gonna add, in this case, we have negative three from the first binomial and four K from the second binomial. So we have negative three multiplied by four K and don't miss those negative signs. OK? Those are important to include, so that we get the right sign in our resulting expression. Um So make sure you're keeping those negative signs where they should be and this represents our inside term. OK? And then we're gonna add our final term. OK? 1, 1 more term. And that's gonna be made up of the last. So the last term from the first binomial is negative three. The last term from the second binomial is negative one. So we have negative three multiplied by -1. And again, this represents our last term or the L in foil. So now we've completed the foil method. We've done F O I and L we've done the multiplication. What's left to do is to simplify the expression starting with the first term, five K multiplied by four K. Yeah. So when the co with the coefficient we have five multiplied by four, this will give us a coefficient of 20, then we have K multiplied by K. You recall when we multiply two things together that have the same base the exponents at and so we get K to the exponent one plus one and then we add the next term. Now the next term we have five K multiplied by negative one. So we get -5K. So we're gonna subtract 5K in our expression. Moving to the inside term negative three multiplied by four K, it gives us negative 12 K. So we subtract 12 K in our expression in our final term. The last term negative three multiplied by negative one that gives us positive three. So plus three in our expression. So we've simplified a little bit, we have a few more things we can do. So let's do one more step here, we have 20 multiplied by K to the exponent one plus one. We can simplify that exponent and write this as 20 k squared. We have negative five K minus 12 K. We can combine those two terms that's gonna be negative 17 K. So we subtract 17 K and then we have our plus three, that constant term at the end. And now we have a single K squared term, a single K term, a single constant term. There's no more simplifying we can do. And so this is the final expression we were looking for if we compare this with our answer choices, we found using the foil method of multiplication. The product of the binomials we were given is 20 K squared minus 17 K plus three, which corresponds with answer choice. C 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.(3y−4)(2y−1)

Key Concepts

FOIL Method

Binomials

Distributive Property

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