Practice Binomial Theorem in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The binomial theorem gives the expansion of (a + b)^n as a sum of terms involving binomial coefficients: (a+b)^n = sum of C(n,k) * a^(n-k) * b^k. Each coefficient \binom{n}{k} counts the number of ways to choose k copies of b from n factors.

Each term of (a+b)^n picks 'a' or 'b' from each factor. \binom{n}{k} counts how many ways to pick k b's.

Example 1

medium
Expand (x + 2)^3 using the Binomial Theorem.

Example 2

hard
Find the coefficient of x^3 in the expansion of (2x + 3)^5.

Example 3

easy
Expand (a + b)^4 using Pascal's triangle.

Example 4

medium
What is \binom{6}{2}?