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The Binomial Theorem

The Binomial Theorem. What about the coefficients of each term? Is there a pattern there?. Find the patterns:. 1. (x + y) 0. (x + y) 0. x 1 + y 1. x + y. (x + y) 1. (x + y) 1. x 2 + 2xy + y 2. (x + y) 2. (x + y) 2. (x + y) 3. (x + y) 3.

hermione-hodge
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The Binomial Theorem

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  1. The Binomial Theorem

  2. What about the coefficients of each term? Is there a pattern there? Find the patterns: 1 (x + y)0 (x + y)0 x1 + y1 x + y (x + y)1 (x + y)1 x2 + 2xy + y2 (x + y)2 (x + y)2 (x + y)3 (x + y)3 x3 y0 + 3x2 y1 + 3x1 y2+ x0 y3 x3 + 3x2 y1 + 3x1 y2+ y3 x3 y0 + 3x2 y1 + 3x1 y2+ x0 y3 x3 + 3x2 y + 3xy2+ y3 (x + y)4 (x + y)4 x4 + 4x3 y + 6x2 y2 +4xy3 + y4 Notice how the exponents of each term sum to “ n “. (x + y)6 x6 + 6x5 y + 15x4 y2 +20x3 y3 + 15x2 y4 + 6x1 y5 + y6

  3. What about the coefficients of each term? Is there a pattern there? 0 1 1 1 1 1 2 1 2 1 1 3 3 3 1 4 6 4 1 4 10 5 1 1 5 10 5

  4. Finding the Coefficient of a Binomial using a Formula. n =

  5. Finding the Coefficient of a Binomial using a Formula. 6 = = x 3 = x x

  6. Finding the Coefficient of a Binomial using a Formula. =

  7. Finding the Coefficient of a Binomial using a Formula. 5 = 2 x = x x

  8. What about the coefficients of each term? Is there a pattern there? 0 1 1 1 1 1 2 1 2 1 1 3 3 3 1 4 6 4 1 4 10 5 1 1 5 10 5 5 5 5 5 5 5

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