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# Pre-Cal 40S May 12, 2009

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Working with the binomial theorem.

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### Pre-Cal 40S May 12, 2009

1. 1. Poker Combinatorics or How likely is THAT?!? Red Hot Poker by ﬂickr user kimberlyfaye
2. 2. The Binomial Theorem ... Algebraically Combinatorically Notice the patterns ... (1) The coefﬁcient of the term is: (2) The exponent on a is given by: [n - (i - 1)] (3) The exponent on b is given by: i - 1 (4) This relation holds for each term in the expansion: [exponent on a] + [exponent on b] = n (5) The number of terms in any binomial expansion is: n + 1
3. 3. Evaluate each term ... n! nC r = (n-r)!r!
4. 4. Pascal's Triangle Can you ﬁnd the Hockey Stick pattern?
5. 5. Any individual term, let's say the ith term, in a binomial expansion can be represented like this: Example: Find the 4th term in the expansion of
6. 6. Determine the indicated term in each expansion. (a) the 8th term in the expansion of
7. 7. Example: Find the term that contains x7 in the expansion of
8. 8. Find the term that contains in the expansion of:
9. 9. Find the term that contains in the expansion of: