In Exercises 152–153, a polynomial is given in factored form. Use...

Question

In Exercises 152–153, a polynomial is given in factored form. Use multiplication to find the product of the factors.

(x + 4)(3x − 2y)

Accepted Answer

Hey, everyone in this problem, we're asked to find the product of the two binomials. The first binomial we're given is A plus eight and that's multiplied by the second binomial or a -7 b. We're given four answer choices. Option A four A squared plus seven A B minus 32 A minus 56 B. Option B four A squared minus seven A B plus 32 A minus 56 B. Option C four A squared plus seven A B plus 32 A minus B in option D four A squared minus seven A B minus A minus 56 B. We're gonna start by rewriting what we were given. We have the binomial A plus eight multiplied by the binomial 4 A -7 B. Now we have two binomials multiplied together. OK. So we can use the boil method to do this multiplication. Can you recall the foil method first, outside, inside last? And that's going to indicate which terms of our binomials to multiply together, add up all of those terms to get a resulting expression. So the F and foil stands for first. So we want to multiply the first term of the first binomial by the first term of the second binomial, that's gonna be a multiplied by 4 a. And this represents our first terms for the F in foil. Then we're gonna add, next is the o the outside terms. So we're gonna take the outermost terms. The one on the far left, the one on the far right of our expression from the first binomial on the far left, we have A and the far right is our second binomial. We have negative seven B. So we have a multiplied by -7 b. This represents our outside terms. Next, we do the I in foil. So the inside terms, so we just did the outside terms. Now we're gonna take the other terms, the ones on the inside, closest together between the binomials. So from the first binomial, we have eight. From the second binomial, we have four A. So we get eight multiplied by 4 a. Again, this represents our inside terms or the eye and foil. And finally, we add, and we want to do the last terms. Now, so we're gonna multiply the last term of the first binomial eight and the last term of the second binomial negative seven B eight multiplied by -7 B. This is our last term or the L in foil. So now we've done that multiplication, we've used the foil method. And what's left to do is to simplify our expression starting with our first term A multiplied by 4 a recall that when we multiply two things together with the same base, we can add the exponents. So we get four A to the exponent 1 plus 1. Our next term A multiplied by negative seven B. So this is gonna give us negative seven A B. Our next term eight multiplied by 4 a. This is equal to 32 a in the final term, eight multiplied by -7 B. This is equal to -56 b. Mhm. So we have our expression that's mostly simplified. There's one more step, we can simplify the exponent in this first term. So we have A to the exponent one plus one that's gonna be A squared. And so our expression becomes four A squared minus seven A B plus 32 A minus 56 B. And this is the expression that is simplified as we can get it the product of those two binomials. So if we compare this to our answer choices, we see that this corresponds with answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 152–153, a polynomial is given in factored form. Use multiplication to find the product of the factors. (x + 4)(3x − 2y)

Key Concepts

Polynomial Multiplication

Factored Form

Combining Like Terms

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