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The Binomial Theorem

The Binomial Theorem. Questions:. Put (x+y) 2 in standard form Put (x+y) 3 in standard form Put (x+y) 4 in standard form. Pascal’s Triangle. is a triangle of numbers, each new number being the sum of the two above it.

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The Binomial Theorem

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  1. The Binomial Theorem

  2. Questions: • Put (x+y)2 in standard form • Put (x+y)3 in standard form • Put (x+y)4 in standard form

  3. Pascal’s Triangle • is a triangle of numbers, each new number being the sum of the two above it. • Each Row of Pascal’s triangle contains coefficients for the expansion of (a+b)n • Let’s look at Pascal’s Triangle • http://www.shodor.org/interactivate/activities/pascal1/

  4. Now \

  5. Use Pascal’s Triangle to expand (a+b)6 Use Pascal’s triangle to get the coefficients. Then with the exponents a will decrease as b will increase.

  6. Use Pascal Triangle to expand: (x-2)3

  7. Review of Combinations

  8. Another way to expand in called the Binomial Theorem

  9. Let’s look at (a+b)4

  10. (x-2)5

  11. Homework P294 2,6,16,20,22

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