Binomial Theorem

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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

 

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 7^th term of

Example:
Using the formula

The Binomial Theorem - Example 1

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

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Binomial Theorem - Example 2

Example:
Expand
a) (3x - y)³

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

Example:
Expand
(x + 2)⁵

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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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