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

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Presentation on theme: "Binomials raised to a power! The Binomial Theorem Pascal Triangle."— Presentation transcript:

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

2 Combination 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. n C r or n C r or C n r

3 n C r = 5 C 2 = Combination

4 Your Turn 7C37C3 12 C 7 9C59C5 6C16C1 14 C 9 35 792 126 6 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....

8

9 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. The Binomial Theorem (Binomial expansion)


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