 # 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 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:

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a) (a + b)5
b) (2 + 3x)3

Solution: Example:

Find the 7th term of Solution:

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

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