We can use the binomial theorem to expand and simplify expressions of the form
where n is any positive whole number.
The general expansions is
Example:
We evaluate the coefficient of each power of
and simplify:
Example:
which simplifies to
then
Suppose we have an expansion. We know
and 
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 of
equals the coefficient of
The coefficient ofis 
The coefficient ofis 
Equate these:
Now cancel where possible
