Pg. 606 Homework Pg. 606 #11 – 20, 34 #1 1, 8, 28, 56, 70, 56, 28, 8, 1 #2 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1 #3 a5 + 5a4b + 10a3b2 + 10a2b3.

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Pg. 606 Homework Pg. 606 #11 – 20, 34 #1 1, 8, 28, 56, 70, 56, 28, 8, 1 #2 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1 #3 a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5 #4 a6 – 6a5b + 15a4b2 – 20a3b3 + 15a2b4 – 6ab5 + b6 #5 x4 + 8x3y + 24x2y2 + 32xy3 + 16y4 #6 2187x7 – 5103x6y + 5103x5y2 – 2835x4y3 + 945x3y4 – 189x2y5 + 21xy6 – y7 #8 a4 – 8a3b2 + 24a2b4 – 32ab6 + 16b8

11.3 Binomial Theorem Expand: (3x– y4)3 (4x + y0.5)4

11.3 Binomial Theorem Binomial Coefficients Pascal’s Triangle works for relatively small values, but what if you want to expand something much larger? We use a factorial to do so! n! = 1 • 2 • 3 • … • n 3! = 8! = If n and r are two nonnegative integers, the number called the binomial coefficient n choose r is defined by:

11.3 Binomial Theorem Binomial Theorem Expand: (x + y)5

11.3 Binomial Theorem Binomial Theorem Examples: Find the y12 term of: (x + y)15 Find the coefficient of the given term in the binomial expansion: x3y4 term, (x + y)7 x8 term, (x + 5)11 x10 term, (x – 6)14

11.3 Binomial Theorem Binomial Theorem Examples: Given: (2x – 1)10 Find the coefficient of the given term in the binomial expansion: x3 x8 x5