# 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:

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 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

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