1. The Binomial Theorem
Pascal Triangle
Binomials raised to a power!

2. Combination A symbol is introduced to represent this selection.
There are 5 top students in this class. If I would like to select 2 students out of these five to represent this class. How many ways are there for my choice?
List of the combinations ( order is not considered) :
(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)
A symbol is introduced to represent this selection.
nCr or nCr or Cnr

3. Combination
nCr =
5C2 =
5C2 =
5C2 =

4. Your Turn
7C3 35
12C7
792
9C5
126
6C1 6
14C9
2002

5. Pascal Triangle

6. The binomial theorem is used to raise a binomial (a + b) to relatively large powers. To better understand the theorem consider the following powers of (a+b):

7. Using these patterns the expansion of looks like
...
and the problem now comes down
to finding the value of each coefficient.

9. The Binomial Theorem (Binomial expansion)
Coefficients are arranged in a Pascal triangle.
Summation of the indices of each term is equal to the power (order) of the expansion.
The first term of the expansion is arranged in descending order after the expansion.
The second term of the expansion is arranged in ascending order order after the expansion.
Number of terms in the expansion is equal to the power of the expansion plus one.