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.

(7x³+5)(x²−2)

Accepted Answer

Hello, everyone. Using the foil method of multiplication. What is the product of the following binomials? We have open parentheses. Three Y cubed plus eight, closed parentheses, multiplied by open parentheses. Y squared minus three closed parentheses. Our answer choices are a three Y raised to the fifth power minus nine Y cubed plus eight Y squared plus 24 B three Y raised to the fifth power minus nine Y cubed plus eight Y squared minus 24 C three Y raised the fifth power plus nine Y cubed minus eight Y squared plus 24 D three, Y raised the fifth power plus nine Y cubed minus eight Y squared minus 24. I'm going to rewrite my binomials. So I have open parentheses. Three Y cubed plus eight, closed parentheses multiplied by open parentheses. Y squared minus three, Y closed parentheses. Recall that foil stands for first, outer, inner and last. And that's the order we're gonna multiply in. So first is the first term in both binomials. So in this case, three Y cubed multiplied by Y squared says alpha first. So the three remains Y cubed multiplied by Y squared when we have a like base and multiply we add our exponents. So we get three Y to the fifth. And that's F for first, outer would be three Y cubed multiplied by negative three and negative three, multiplied by three is negative nine. And then Y cubed has nothing to change it. So it stays Y cubed. And that's O for outer, next is I for in and that's gonna be eight multiplied by Y squared. That will be a positive eight Y squared because there's no way to change either of those things. They just end up sitting next to each other. So that's our eye and foil. And last is the last term in each binomial. So eight multiplied by negative three, which would result in a negative 24. So that's our L. So now that we have all foil multiplied out, I wanna see if there are any common terms that we can combine. Um I do not see any like terms. So this is our product. It is three Y raise to the fifth power minus nine Y raise to the third power plus eight Y squared minus 24. And that's answer choice B have a nice day.

In Exercises 35–54, use the FOIL method to multiply the binomials. (7x³+5)(x²−2)

Key Concepts

Binomials

FOIL Method

Combining Like Terms

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