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.

(3xy−1)(5xy+2)

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? By no meals? The first binomial we're given is 3 HK -1. This is multiplied by the second binomial six H K plus five. We're given four answer choices. Option A 18 H squared K squared minus 13 H K minus five. Option B 18 H squared K squared plus 13 H K minus five. Option C 18 H squared K squared minus nine H K minus five. In option D 18 H squared K squared plus nine H K minus five. We're gonna start by writing out the binomials we were given. So we have three H K minus one, multiplied by the second binomial six H K plus five. We're asked to use the foil method and recall that the foil method tells us to take the first terms of our B binomials and multiply them together. Take the outside terms, multiply them together, take the inside terms, multiply them together and then take the last terms and multiply them together. This is gonna give us the four terms of our resulting expression and we're gonna add those four terms together. All right. So let's go ahead and do that. So we're gonna start with the first terms. OK? So the first term of our first binomial is 3 HK, the first term of our second binomial is six H K. And so we get three H K multiplied by six H K and this represents our first terms or the F in foil. Now, we're gonna add, and our next term is gonna come from the outside. So we're gonna take the far left term from the first binomial, the far right term from the second binomial. So from the first Bino meal on the far left, we have three H K on the far right, the second binomial, we have five. So we have 3 HK multiplied by five. And this represents our outside terms are the O and foil. Now we're gonna add, we're gonna add the inside terms. So we're gonna take the innermost terms from each binomial, the ones that are closest together from the first binomial. We have negative one. From the second binomial. We have 6 HK. They have negative one multiplied by 6 HK. This represents our inside terms or the eye and foil. We're gonna add, this is our final term and it's gonna be made up of the last terms. So we're gonna take the last term of the first binomial, the last term of the second binomial and multiply them together, we get negative one multiplied by five. And this represents the last terms for the L in foil. So now we've applied the foil method, we've done the multiplication. All we have left to do is to simplify this expression. Starting with our first term, we have 3 HK multiplied by 6 HK, starting with the constant coefficient, we have three multiplied by six. So the coefficient is going to be 18. We have an H multiplied by an H recall when we multiply two things with the same base, the exponents add. So we get H to the exponent one plus one. And then we have the same with the K, we have K multiplied by K. So we get K to the exponent one plus one as well. So 18 H to the exponent one plus one K to the exponent one plus one. And then we're gonna add our next term. Our next term we have 3 HK multiplied by bye. This is gonna give us 15 HK our next term negative one multiplied by six H K. So we get negative six H K. So we subtract mm in our final term, we have negative one multiplied by five that gives us negative five. And so we subtract five in our expression, we can simplify this a little further. So let's do another step in this first term, we can simplify the exponents. So we have H to the exponent one plus one, we can write as H squared and K to the exponent one plus one, we can write as K squared. And so we have 18 H squared K squared plus, we have 15 HK -6 HK. We can combine these together and we have plus 9 HK and then our constant term at the end -5. And now this is as simple, simplified as we can get it. So this is the resulting expression we were looking for, we compare this to our answer choices. We found using the foil method of multiplication. The product of the binomials we were given is 18 H squared K squared plus nine H K minus five, 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. (3xy−1)(5xy+2)

Key Concepts

FOIL Method

Binomials

Distributive Property

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