Recall that the binomial theorem is an algebraic method of expanding a binomial that is raised to a certain power, such as
The coefficients that appear in the binomial expansion are called binomial coefficients. These are usually written
The coefficient of a term
Note that although this formula involves a fraction, the binomial coefficient
In calculating coefficients, recall that the factorial of a non-negative integer
Finally, you may recall that the factorial
Example: Use the binomial formula to find the expansion of
Start by substituting
In order to solve this, we will need to expand the summation for all values of
Recall that
Now we must evaluate each of the remaining combinations:
Substituting these integers into the expansion, we have: