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The Binomial Theorem and Pascal’s Triangle

The Binomial Theorem and Pascal’s Triangle. Integrated Math 4 Mrs. Tyrpak. Consider Binomial Expansion. Examine and Organize the Coefficients. This array of numbers is: __________. Connection: Pascal’s Triangle and Combinations.

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The Binomial Theorem and Pascal’s Triangle

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  1. The Binomial Theorem and Pascal’s Triangle Integrated Math 4 Mrs. Tyrpak

  2. Consider Binomial Expansion

  3. Examine and Organize the Coefficients This array of numbers is: __________

  4. Connection: Pascal’s Triangle and Combinations Compute C(4,2). What row and what entry is this in Pascal’s triangle? Compute C(6,4). Row: _____ Entry: _____

  5. Generalization

  6. Using Combinations for Binomial Expansion

  7. Practice: Find the coefficient of all the terms in

  8. Binomial Theorem For any positive integer n,

  9. Using the Binomial Theorem Expand:

  10. Notice the Symmetry in Pascal’s Triangle What can we conclude about combinations based on this and the binomial theorem? Prove this using factorial formulas.

  11. Reminders for Mathematicians Stay Focused! It is more about improving your logic and mathematical reasoning than memorization. Make sure you are completing your extension and enrichment assignments.

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