Expanding brackets such as (3+2x)^5 is tedious by expanding the brackets one by one. Fortunately there is a quicker method using the binomial theorem. It states,
where n is an integer greater than or equal to one.
Example: Expand
then
which simplifies to
and further to
Example: Expand
then
This simplifies to
We may be asked to solve questions involving the coefficients. For example, the coefficient of
in the binomial expansion of
is equal to 3 times the coefficient of
Find n.
Using the binomial expansion, the coefficient ofis
Using the binomial expansion, the coefficient of
is
Hence we can write down the equation
Now we have to perform some trickery:
