# Binomial Expansion

Binomial Expansion refers to expanding an expression that involves two terms added together and raised to a power, i.e. . In the simple case where n is a relatively small integer value, the expression can be expanded one bracket at a time:

**Example 1** –

**Example 2** –

using the expansion above.

Expanding by hand for larger n becomes a tedious task. The Edexcel Formula Booklet provides the following formula for binomial expansion:

where

for when , i.e for when n is a positive integer.

**Example 3** – Find the first three terms, in descending powers of x, in the binomial expansion of .

This can be done using the formula above. Perform a direct substitution as follows: a=2x, b=4 and n=5 and take the first three terms.

Note that

and

and so the formula becomes

Note that if the question says ascending powers of x, then a and b can be switched over so that the powers of x are increasing instead.