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Binomial Theorem

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

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

Solution:

Using the formula




The Binomial Theorem - Example 1
Examples:
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?
Examples:
Expand
(x + 2)5
The Binomial Theorem Using Combinations
How to expand a binomial raised to a power using the binomial theorem?
Examples:
Expand
(2x - 3)4


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