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.(x−3y)(2x+7y)

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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. The 1st 1 is M -4 K and it's multiplied by the second binomial two M plus five K. We have four answer choices. Option A is negative. The entire expression of 20 K squared plus three K M minus two M squared. Option B negative the entire expression of 20 K squared plus 20 K minus two M minus two M squared. Option C 20 K squared plus three K M minus two M squared. In option D 20 K squared plus K minus two M minus two M squared. We're gonna start by rewriting the binomials we've been given. So we have the first one M minus four K multiplied by the 2nd 12 M plus five K. And we're asked to use the foil method and recall that the foil method tells us to take the first terms of the binomials multiply them together, the outside terms of our binomial multiply them together, the inside terms of our binomial multiply them together. And the last terms of our binomial and multiply them together, that gives us the four terms of our resulting expression. And we add those four terms up to get that expression. So foil first, outside, inside last. So let's go ahead and apply that. So the first term from our first expression, our first binomial is M, the first term from our second binomial is two M. So we get M multiplied by two M which represents the first terms or the F in foil. Then we're gonna add the next term we're gonna take is the outside terms. So we're gonna take the far left term from the first expression which is N the far right term of the second binomial, which is 5K and multiply them together M multiplied by five K. And this represents our outside terms or the O in foil. Next, we're taking the inside terms. So the inside terms are gonna be the terms that are closest together between those two binomials. So from the first binomial, we have negative 4K from the second binomial, we have two M so negative or K multiplied by two M. This represents our inside terms or the eye and foil. And then we're gonna add, we have one final term here and that's gonna be made up of the last terms. So we're gonna take the last term of the first binomial negative four K, the last term of the second binomial five K. So we have negative 4 k multiplied by five K. This represents our last terms or the L in Foyle. OK. So now we've applied the foil method. We've done the multiplication. We're just left to simplify this expression. Starting from the left, we have M multiplied by two M. This gives us two M and recall when we have M multiplied by M the same base, the exponents add so we get two M to the exponent one plus one. Our next term is M multiplied by 5K. You can write this as 5 km. Our next term 4 k multiplied by two M. This gives us negative eight K M. OK. We had negative four K multiplied by two M negative eight K M. We're gonna subtract 8 KM in our expression. And then we have negative four K multiplied by five K. This gives us negative 20 K and so we subtract whoops negative 20 sorry K multiplied by K. Same as we did with the first terms. When we multiply with the same base, the exponents add. So we end up with not negative 20 K but negative 20 K to the exponent one plus one. Now we can simplify this expression a little bit. So let's do another step and simplify our expression. We have two M to the exponent one plus one. We can simplify that exponent and write it as two M squared five K M minus eight K M. It gives us negative three K M. And so we can write this as subtract three K M and negative 20 k to the exponent one plus one can simplify that exponent and write negative 20 k squared. So now we have this expression, we can't simplify any further. It's two M squared minus three K M minus 20 k squared. Now, if we compare this with our answer choices, you see that all of the answer choices have the negative factored out of 20 K word. OK. So let's go ahead and factor a negative out of our expression to try to fit with the answer choices we've been given, we're gonna factor it a negative and we're just gonna rearrange this equation in the answer choices. They have the K squared term first, then the K M term and then the M squared term. So let's write it in the same order. So it's easier to compare. So we factor out a negative and we write the K squared term first. We're gonna have negative and then brackets 20 k squared Plus 3 KM -2 M Squared. We factored out that negative, we rearranged our terms and we now have an expression that matches one of the answer choices. So this is gonna be our resulting expression. Using the foil method. We found the product of these binomials we were given and we found that that product is negative. The expression 20 K squared plus three K M minus two M squared, which corresponds with answer choice. A 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.(x−3y)(2x+7y)

Key Concepts

Binomials

FOIL Method

Combining Like Terms

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