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.(7xy+1)(2xy−3)

Accepted Answer

Hey, everyone in this video, we're gonna be walking 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 three H K plus one. Then it's multiplied by the second binomial 6 HK -5. 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 rewriting the binomials we've been given. So we have the first binomial three H K plus one multiplied by the 2nd Binomial 6 HK -5. We're asked to use the foil method and we're called it, the foil method tells us to take the first terms of our binomials and multiply them together, take the outside terms of our expression and multiply them together, take the inside terms of our expression and multiply them together and then take the last terms of our expression and multiply them together. And this will give us four terms. Can we add those terms together to get the result of the multiplication? So let's go ahead and do this. Let's apply this foil method starting with F first. So we're gonna take the first term of the first, final meal three H K multiply it by the first term of the second vino mule six H K, we have 3 HK multiplied by 6 HK. And this represents our first terms for the F and foil. Now we're going to add, the next term is gonna come from the outside. So we're gonna take the outermost terms in our expression, the one on the far left and the one on the far right. So from the first binomial on the far left, we get 3 HK and from the second binomial on the far right, we have negative five. So we get 3 HK multiplied by -5. And this represents our outside terms or the O in foil. Now we add, the next term is gonna come from the inside. We're gonna take the inside terms of our expression, the ones closest together and multiply them. So from the first pin Nomi, we have one, from the second B meal, we have six H K, we have one multiplied by 6 HK. Then this represents our inside terms or the eye in foil. Then we add, this is our final term and this is gonna come from the last terms. We're gonna take the last term of the first binomial one, the last term of the second binomial negative five multiply them. So we have one multiply it by -5. This represents our last terms. And the resulting expression, we've applied our file method and we've done the multiplication and now we're left with just simplifying. So starting with our first term, 3 HK multiplied by 6 HK, starting with the coefficient, we have three multiplied by six, which is going to give us 18. We also have H multiplied by H recall when we multiply two things with the same base, we add the exponent. So we can write this as H to the exponent one plus one. And we also have K multiplied by K in this term. So similarly to the H, we get K to the exponent one plus one. So 18 H to the exponent one plus one K to the exponent one plus one. Our next term three H K multiplied by negative five. This gives us negative 15 H K. Our next term one multiplied by 6 HK. This plus 6 HK in our expression in our last term, one multiplied by -5. This gives us -5. So we've simplified quite a bit but we have a few more steps we can do. OK. So starting with our first term, we can simplify these exponents. So we have 18 to the exponent H sorry H to the exponent one plus one. And this is 18 H squared. And we also have K to the exponent one plus one, which is K squared. So 18 H squared, K squared, we have minus 15 H K plus six H K. We can combine those terms, we're gonna get minus nine H K and we have our constant -5 that we can't simplify any further. And this is our simplified expression. We can't simplify any further. This is the result we were looking for if we compare this to the answer choices, OK. Using the foil method, we found that the product of the binomials we were given is 18 H squared K squared minus nine H K minus five, 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.(7xy+1)(2xy−3)

Key Concepts

FOIL Method

Binomials

Distributive Property

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