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Find the indicated term of the binomial expansion…

01:13

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Problem 36 Hard Difficulty

Find the indicated term of the binomial expansion. See Examples 4 and 5.
$$(a-b)^{14}, 6 \text { th term }$$

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Algebra

Algebra for College Students

Chapter 13

Sequences and Series

Section 5

Binomial Expansions

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Video Transcript

We have this formula for finding the case term in a binomial expansion, but it's pretty confusing looking so down here I am trying to make it more concrete for finding the sixth term. You're going to have fives in your formula and all four of these places. So the problem that we're doing is finding the sixth term of a minus B to the 14th. Think of a minus beat of the 14th as a plus negative B to the 14th. OK, so using the formula, we're going to have 14 factorial divided by 14 minus five factorial times five factorial. Remember from down here we said that if you're doing 1/6 term, you end up using five in there, and then that's gonna be multiplied by a to the 14 minus five power times, the opposite of B to the fifth power. Now it's simplify that. So the factorial part of it works out to be 2002 and then we have a to the ninth power, and we have the opposite of B to the fifth. So because you're taking a negative and raising it to the fifth, it's going to work out to be negative. So put the negative in front of the 2002. So that means we have negative 2000 to 8 to the ninth B to the fifth.

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