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.

(5x+3)(2x+1)

Accepted Answer

Hey, everyone. Welcome back. Using the foil method of multiplication. What is the product of the following binomials? The first binomial we're given is six H plus five and that is multiplied by the second binomial three H plus two. We're given four answer choices. Option A 12 H squared plus H plus 15. Option B 18 H squared plus H plus 15. Option C 12 H squared plus H plus 10 and option D 18 H squared plus 27 H plus 10. Let's start by rewriting our binomials six H plus five, multiplied by three H plus two. Now, we're asked to use the foil method. What foil method stands for is first outside, inside last. Ok. So what we're gonna do is we're gonna take the first term of each binomial multiply them together. We're gonna take the outside terms, multiply them together, the inside terms multiply them together. And finally the last terms and multiply them together. And that is gonna give us the four terms of our resulting expression. So let's get started. The first term of the first binomial sticks. H Multiplied by the first term of the second binomial three H. OK. And this represents our first terms or the F in foil and we're gonna add the next term and the next term is going to be the outside. So we're gonna take the outside of our expression. So on the outer left side, we have the term six H. On the outer, right side, we have the term two. So we have six h multiplied by two. And this represents, are outside term, maybe the O and foil. Next, we have our inside term. So we're gonna take the two innermost terms from the first binomial. That's five. And we multiply that to the term from the second binomial three H. So five multiplied by three H. This represents our inside term or the I and foil. And then we have our last term. So we're gonna take the last term from the first binomial by and multiply it to the last term of the second binomial two. So we get five multiplied by two. Then this is our last term or the L in foil. So now we've done the multiplication, we've used the foil method. All that's left now is to simplify. So in our first term, we have six H multiplied by three H A six, multiplied by three is gonna give us a coefficient of 18. And then we have H multiplied by H recall when we multiply two things with the same base, we add the exponent. So we get 18 H to the exponent one plus one. We're gonna add this to our outside term and our outside term is six h multiplied by two. This gives us 12 h and we add our inside term five multiplied by three H. This gives us 15 H And we add our last term five multiplied by two, which gives us 10. OK. We're really close, but we have a little bit more simplifying. We can do, we can simplify the exponent in the first term. And we also have two H terms. So we can combine those into one. Our expression becomes 18 H squared Plus 27 h plus 10. We had 12 plus 15 inch that gives us 27 inch. Now we have our expression, we only have one H square term, one H term and a constant term. So this is as simplified as we can get it. And so that is the result we were looking for comparing this to the answer choices we found using the foil method of multiplication. The product of the binomials is 18 H squared plus 27 H plus 10, 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. (5x+3)(2x+1)

Concetti chiave

FOIL Method

Binomials

Distributive Property

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