Binomial Theorem


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




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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



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