Find the term indicated in the expansion. (2x-3)^6; fifth term

Key Concepts

Binomial Theorem

The Binomial Theorem provides a formula for expanding expressions of the form (a + b)^n. It states that the expansion can be expressed as a sum of terms involving binomial coefficients, which are calculated using combinations. This theorem is essential for determining specific terms in the expansion of binomials, such as the fifth term in (2x - 3)^6.

Binomial Coefficients

Binomial coefficients are the numerical factors that appear in the expansion of a binomial expression. They are denoted as C(n, k) or nCk, representing the number of ways to choose k elements from a set of n elements. In the context of the Binomial Theorem, these coefficients are crucial for calculating the specific terms in the expansion, including the fifth term.

Term Position in Expansion

In the expansion of a binomial expression, each term corresponds to a specific position determined by the powers of the variables involved. The general term in the expansion can be expressed as T(k+1) = C(n, k) * a^(n-k) * b^k, where k is the term index. Understanding how to identify the term position is vital for finding the fifth term in the expansion of (2x - 3)^6.