The Binomial Theorem. (x + y) 0 Find the patterns: 1 (x + y) 1 x + y (x + y) 2 (x + y) 3 x 3 + 3x 2 y + 3xy 2 + y 3 (x + y) 4 (x + y) 0 (x + y) 1 (x +

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The Binomial Theorem

(x + y) 0 Find the patterns: 1 (x + y) 1 x + y (x + y) 2 (x + y) 3 x 3 + 3x 2 y + 3xy 2 + y 3 (x + y) 4 (x + y) 0 (x + y) 1 (x + y) 2 (x + y) 3 (x + y) 4 x 1 + y 1 x 2 + 2xy + y 2 x 3 + 3x 2 y 1 + 3x 1 y 2 + y 3 x 4 + 4x 3 y + 6x 2 y 2 +4xy 3 + y 4 x 3 y 0 + 3x 2 y 1 + 3x 1 y 2 + x 0 y 3 (x + y) 6 x 6 + 6x 5 y + 15x 4 y 2 +20x 3 y x 2 y 4 + 6x 1 y 5 + y 6 Notice how the exponents of each term sum to “ n “. What about the coefficients of each term? Is there a pattern there?

Finding the Coefficient of a Binomial using a Formula.

x x x 3

x x x 2

1 What about the coefficients of each term? Is there a pattern there?

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