Binomial Theorem
In these lessons, we will look at how to use the Binomial Theorem to expand binomial expressions.
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
Note that:
- The powers of a decreases from n to 0.
- The powers of b increases from 0 to n.
- 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
Example:
Expand
a) (a + b)5
b) (2 + 3x)3
Solution:
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
Check out our most popular games!
Fraction Concoction Game:
Master fractions in the lab: mix, add, and subtract beakers to create the perfect concoction!
Fact Family Game:
Complete fact families and master the link between addition & subtraction and multiplication & division.
Number Bond Garden:
Clear the board by matching number pairs that sum to ten in this garden-themed mental math puzzle.
Online Addition Subtraction Game:
Practice your addition and subtraction skills to help the penguin find its mummy.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.