Binomial Theorem
(or Binomial Expansion Theorem)


Most of the syntax used in this theorem should
look familiar. The
notation is
just another way of writing a combination such as _{n}
C _{k }(read "n choose k").

Example 1: Expand . 

Let a = x, b = 2, n = 5 and
substitute. (Do not substitute a value for k.) 
Now, grab your graphing calculator to find those
combination values.
Method 1: Use
the graphing calculator to evaluate the
combinations on the home screen. Remember: Enter the top value of the
combination FIRST. Then hit MATH key, arrow right (or left) to PRB heading, and choose #3 nCr.
Now, enter the bottom value of the combination.
Method 2: Use
the graphing calculator to evaluate the
combinations under the lists.
In L1, enter the values 0 through
the power to which the binomial
is raised, in this case 5.

In L2, enter the combination
formula, using the power of the
binomial as the starting value,
and the entries from L1 as the
ending values.

The coefficients from the
combinations will appear
in L2.

Finding a
Particular Term in a Binomial Expansion
The
r ^{th} term of the expansion of is:
