---
title: Binomial Theorem
description: The binomial theorem provides an algebraic formula for expanding powers of a binomial expression. Learners will understand how to calculate coefficients using combinatorics and apply the theorem to probability and series expansions.
category: mathematics
subcategory: combinatorics
difficulty: beginner, intermediate, advanced
url: /subject/binomial-theorem
---

# Binomial Theorem

The binomial theorem provides an algebraic formula for expanding powers of a binomial expression. Learners will understand how to calculate coefficients using combinatorics and apply the theorem to probability and series expansions.

## Available Resources

1 Courses • 4 Websites

## Websites

### 1. Khan Academy - Binomial Theorem

Khan Academy unit on expanding powers of binomials, with short videos and graded practice. It moves from Pascal's triangle to combinations and the general binomial formula, so learners can expand expressions and find specific coefficients without multiplying everything out.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:binomial-theorem

**Tags:** binomial-theorem, pascals-triangle, combinations, polynomial-expansion, algebra-2

### 2. Brilliant.org - Binomial Theorem

Brilliant wiki article stating the binomial theorem, proving it combinatorially, and working through examples on coefficients, multinomial extensions, and identities. Learners practice finding terms in expansions and applying the theorem to counting and competition-style problems.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://brilliant.org/wiki/binomial-theorem/

**Tags:** binomial-theorem, binomial-coefficients, combinatorics, multinomial-theorem, problem-solving

### 3. Art of Problem Solving - Binomial Theorem

Art of Problem Solving wiki entry giving the binomial theorem with a combinatorial proof, generalizations to non-integer exponents, and a set of past AMC and AIME problems with solutions, preparing students to use binomial expansions in mathematics competitions.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://artofproblemsolving.com/wiki/index.php/Binomial_Theorem

**Tags:** binomial-theorem, binomial-coefficients, combinatorics, competition-math, amc-aime

### 4. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Probabilistic Systems Analysis and Applied Probability (MIT 6.041SC)

**Author:** John Tsitsiklis

Modeling and analysis of uncertainty: probability models, discrete and continuous random variables, Bayesian inference, limit theorems and random processes. Designed for independent study, with lecture videos, slides, recitation and tutorial problems, problem sets and exams with solutions, and TA problem-solving videos.

**Difficulty:** Intermediate | **Price:** Free

**Link:** https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/

**Tags:** probability, random-variables, bayesian-inference, limit-theorems, random-processes, statistical-inference

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