Binomial Expansion

Binomial Expansion refers to expanding an expression that involves two terms added together and raised to a power, i.e. (x+y)^n. In the simple case where n is a relatively small integer value, the expression can be expanded one bracket at a time. See Examples 1 and 2.

Expanding (x+y)^n by hand for larger n becomes a tedious task. The Edexcel Formula Booklet provides the following formula for binomial expansion:




for when n\in{\mathbb N}, i.e for when n is a positive integer. See Example 3 and see Factorial Notation to find out about !

Directly substituting a for x and b for y (whatever they might be), results in finding the expansion. Usually only the first few terms are required. 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.

Example 1

Expand (x+y)^3.

Example 2

Using Example 1 expand (x+y)^4.

Example 3

Find the first three terms, in descending powers of x, in the binomial expansion of (2x+4)^5.