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.(3xⁿ−yⁿ)(xⁿ+2yⁿ)

Accepted Answer

Hello, today we're gonna be using the foil method to multiply the two quantities together. So what we are given is five A to the C power minus B to the C power multiplied by A to the C power plus four B to the sea power. So let's go ahead and foil the two quantities together. We're gonna multiply five AC with A to the power of C and that is going to give us five A to the power of C multiplied by A to the power of C. Then we're going to multiply this term to the second term in the second group. And that is going to give us five A to the power of C multiplied by four B to the power of C. Then we're gonna multiply the second term in the first group with the terms in the second group. So negative B to the power of C times A to the power of C is going to give us negative B to the power of C times A to the power of C. Then multiply this term with the last term in the second group. And that is going to give us negative B to the power of C multiplied by four B to the power of C. So we can do a little bit of simplification here five A to the power of C times four B to the power of C is going to give us 20 A to the C B to the C and negative B to the C times A to the C is going to give us negative A to the C B to the C. And notice that both of these terms have A to the power of C times B to the power of C, we can combine them into a single term and 20 minus one is going to give us 19 A to the C B to the sea. And for the first and last term, we can go ahead and simplify this by using the addition rule for exponential values. And that states that if you have two exponential values A to the power of M multiplied by A to the power of N, as long as these exponential values have the same base, you can combine their exponents together as a sum and rewrite this quantity as A to the power of M plus N for five A to the power of C times A to the power of C, we can combine these terms as five A to the power of C plus C. And that is going to give us five A to the power of two C and we can do the same thing on the last term because negative B to the power C times four B to the power C can be coined as negative four times B to the power of C plus C. And that is going to give us negative four B to the power of two C. So combining all of our simplified terms together is going to give us five A to the power of two C plus 19 times A to the power of C times B to the power of C minus four B to the power of two C. And this is going to be the foiled form of the original expression. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 35–54, use the FOIL method to multiply the binomials.(3xⁿ−yⁿ)(xⁿ+2yⁿ)

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