Find the specified n th term in the expansion of the binomial. (7 x-2 y)^15, n=7

Name: Problem 62, Chapter 9: Algebra and Trigonometry Real Mathematics, Real People
Uploaded: 2020-08-05T19:32:04-08:00
Duration: 3 min 4 s
Channel: Ankit Gupta
Description: Find the specified n th term in the expansion of the binomial. (7 x-2 y)^15, n=7

step 1 Okay, here in this case we have been given a binomial which is 7x minus 2y and Its power is 15 a

Find the specified n th term in the expansion of the...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Binomial Theorem

The Binomial Theorem is a fundamental principle in algebra that provides a formula for expanding expressions raised to a power. It expresses the expansion of a binomial raised to any positive integer exponent as a sum of terms involving binomial coefficients and the respective powers of the two terms in the binomial.

General Term Formula

In the context of a binomial expansion, the general term (or the nth term) is given by a formula that incorporates the binomial coefficient and the appropriate powers of each term in the binomial. This formula allows you to calculate any term in the expansion independently, without having to expand the entire binomial.

Binomial Coefficient

A binomial coefficient, often denoted as C(n, k) or 'n choose k', represents the number of ways of selecting k items from a set of n items. It is a key component in the formula for each term in the binomial expansion and is computed using factorial operations.

Term Indexing in Expansion

Understanding how terms are indexed in a binomial expansion is crucial. Typically, the term corresponding to an index k in the expansion of (a + b)^n is the (k+1)th term. Correctly identifying the position of the term ensures that the appropriate powers of each binomial component are applied in the calculation.

Transcript

Please give Ace some feedback