In the expansion of (1 + x)^n, what is the term containing x^4?

₹0.0

Question: In the expansion of (1 + x)^n, what is the term containing x^4?

Options:

Correct Answer: C(n, 4)x^4

Solution:

The term containing x^4 in the expansion of (1 + x)^n is C(n, 4)x^4.

In the expansion of (1 + x)^n, what is the term containing x^4?

In the expansion of (1 + x)^n, what is the term containing x^4?

Step 1: Understand that (1 + x)^n is a binomial expression that can be expanded using the Binomial Theorem.
Step 2: The Binomial Theorem states that (1 + x)^n = Σ (C(n, k) * x^k) for k = 0 to n, where C(n, k) is the binomial coefficient.
Step 3: Identify that we want the term that contains x^4, which means we need to find the term where k = 4.
Step 4: The term for k = 4 in the expansion is given by C(n, 4) * x^4.
Step 5: Therefore, the term containing x^4 in the expansion of (1 + x)^n is C(n, 4) * x^4.

Binomial Expansion – The expansion of (1 + x)^n involves using the binomial theorem to find specific terms in the polynomial.
Binomial Coefficient – C(n, k) represents the number of ways to choose k elements from a set of n elements, which is crucial for determining the coefficients in the expansion.