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10.7 Binomial Theorem Mon Nov 25

10.7 Binomial Theorem Mon Nov 25. Do Now Expand 1) 2) . HW Review: p.897 #1-31. Binomial Expansion. Let’s look at the expansions of the following powers of (a + b)^n:. Patterns of Binomial Expansion. 1) There is one more term than the power of the exponent

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10.7 Binomial Theorem Mon Nov 25

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  1. 10.7 Binomial TheoremMon Nov 25 Do Now Expand 1) 2)

  2. HW Review: p.897 #1-31

  3. Binomial Expansion • Let’s look at the expansions of the following powers of (a + b)^n:

  4. Patterns of Binomial Expansion • 1) There is one more term than the power of the exponent • 2) In each term, the sum of the exponents is equal to the power the binomial is raised • 3) The exponents of A start with the highest and decrease, while the exponents of B start with 0 and increase • 4) The coefficients follow a pattern

  5. Pascal’s Triangle • Pascal’s Triangle describes the pattern of the coefficients: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

  6. Conclusion • Binomial Theorem using Pascal’s Triangle: • For any binomial (a+b) and any natural n, where the constants C are from the (n+1)st row of Pascal’s Triangle

  7. Ex • Expand (a – b)^5

  8. Ex • Expand

  9. You Try • Expand the following • 1) • 2)

  10. Closure • Expand (2 + x)^4 • HW: p.905 #1-19 odds

  11. 10.7 Binomial Expansion and Factorial NotationTues Nov 26 • Do Now • Expand (3x – 2y)^3

  12. HW Review: p.905 #1-19 odds

  13. Disadvantages of Pascal’s Triangle • While Pascal’s Triangle is very useful, as the exponent of the binomial expansion gets bigger, Pascal’s Triangle requires that we compute every row…

  14. Binomial Theorem Using Factorial Notation • For any binomial a + b and any natural number n,

  15. Ex • Expand

  16. Ex • Expand

  17. Total Number of Subsets • When you have n elements, and there is no exact number you want, the total number of subsets is 2^n

  18. Ex • The set {A, B, C, D, E} has how many subsets?

  19. Ex • Wendy’s offers the following condiments on its single hamburger: • {Ketchup, mustard, mayonnaise, tomato, lettuce, onion, pickle} How many different ways can Wendy’s serve a single hamburger?

  20. Closure • Would you rather use Pascal’s Triangle or Binomial Factorization to expand a binomial? Why? • HW: p.905 #1-11 odds (new way) 31-34

  21. 10.7 ReviewWed Nov 27 • HW Review

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