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Warm-Up 4/7

Warm-Up 4/7. 1. E. Q&A on assignment. 1, 3, 7, 5. 1, 3, 7, 5. 2, 4, 7, 6. 2, 4, 6. Rigor: You will learn how to use Pascal’s Triangle and the Binomial Theorem to expand a binomial. Relevance: You will be able to use these skills in future math courses. 10-5 Binomial Theorem.

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Warm-Up 4/7

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  1. Warm-Up 4/7 1. E Q&A on assignment.

  2. 1, 3, 7, 5 1, 3, 7, 5 2, 4, 7, 6 2, 4, 6

  3. Rigor:You will learn how to use Pascal’s Triangle and the Binomial Theorem to expand a binomial.Relevance: You will be able to use these skills in future math courses.

  4. 10-5 Binomial Theorem

  5. nCr= n(math) (>) (>) (>) (3) r 3C2 = 3 4C0 = 1 6C4 = 15 7C7 = 1 8C2 = 28 5C1 = 5

  6. Pascal’s Triangle

  7. Binomial Theorem:The binomial expansion of (a + b)nfor any positive integer n is: 1st term r = 0, 2nd termr = 1, 3rd term r = 2, 4th term r = 3, …

  8. Example 1a: Use Pascal’s Triangle to expand the binomial. Step 1 Write series omitting coefficients. Step 2 Use a row of numbers in Pascal’s Triangle as the coefficients.

  9. Example 1b: Use Pascal’s Triangle to expand the binomial. Step 1 Write series omitting coefficients. Let Step 2 Use a row of numbers in Pascal’s Triangle as the coefficients.

  10. Example 2: Use Pascal’s Triangle to expand the binomial. Step 1 Write series omitting coefficients. Let Step 2 Use a row of numbers in Pascal’s Triangle as the coefficients.

  11. Example 3: Find the coefficient of the 5th term in the expansion of . r = 4 b = b n = 7 a = a

  12. Example 4: Find the coefficient of in the expansion of . r = ? b = – 3y n = 9 a = 4x r = 2

  13. Example 6: Use the Binomial Theorem to expand the binomial. b = – y n = 4 a = 3x (1)

  14. Example 7: Represent the expansion using sigma notation. b = – 7y n = 20 a = 5x or

  15. math! • 10-5 Assignment: TX p633, 8-24 EOE & 36-44 EOE • Assignment: Review 2-5 & 2-6 1-18 all • Test on 2-5, 2-6, 6-4 & 10-5 Thursday 4/10

  16. Example 6b: Use the Binomial Theorem to expand the binomial. b = q2 n = 5 a = 2p (1) (1) =

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