Binomial Theorem


In these lessons, we will look at how to use the Binomial Theorem to expand binomial expressions.




Share this page to Google Classroom

Related Pages
Binomial Expansions Examples
More Lessons for Algebra

Binomials are expressions that contain two terms such as (x + y) and (2 – x).

The Binomial Theorem states that

Binomial Theorem

Note that:

  1. The powers of a decreases from n to 0.
  2. The powers of b increases from 0 to n.
  3. The powers of a and b always add up to n.

Binomial Coefficient

In the expansion of (a + b)n, the (r + 1)th term is

Binomial Coefficient

Example:
Expand
a) (a + b)5
b) (2 + 3x)3

Solution:
Binomial Theorem Example

Example:
Find the 7th term of

Example:
Using the formula





** The Binomial Theorem - Example 1**

Example:
Expand
a) (a + b)5
b) (x + 1)5

** Binomial Theorem - Example 2**

Example:
Expand
a) (3x - y)3

**The Binomial Theorem Using Combinations **
How to expand a binomial raised to a power using the binomial theorem?

Example:
Expand
(x + 2)5

**The Binomial Theorem Using Combinations **
How to expand a binomial raised to a power using the binomial theorem?

Example:
Expand
(2x - 3)4



Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget



We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.