The Binomial Theorem Pascal Triangle Binomials raised to a power!

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Presentation transcript:

The Binomial Theorem Pascal Triangle Binomials raised to a power!

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

Combination nCr = 5C2 = 5C2 = 5C2 =

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

Pascal Triangle

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):

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

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.