## The Binomial Expansion

We can use the binomial theorem to expand and simplify expressions of the formwhere n is any positive whole number.

The general expansions is

Example:

We evaluate the coefficient of each power ofand simplify:

Example:

which simplifies to

then

Suppose we have an expansion. We knowand but not n. If we have a relationship between the coefficients we may be able to form an equation to find n. Suppose in the expansion below we know that the coefficient ofequals the coefficient of

The coefficient ofis

The coefficient ofis

Equate these:Now cancel where possible