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11.8 The General Binomial Expansion

11.8 The General Binomial Expansion. New notation:. Recall . Use Calc:. 1. 1. 1. Pascal’s. 1. 2. 1. 1. 3. 3. 1. 1. 4. 6. 4. 1. Ex 1) Expand (a + b) 3. Look!. Matches exponent!!. Ex 2) Find the 13 th term of the expansion (x + y) 15. Look at 2 nd variable:.

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11.8 The General Binomial Expansion

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  1. 11.8 The General Binomial Expansion

  2. New notation: Recall Use Calc: 1 1 1 Pascal’s 1 2 1 1 3 3 1 1 4 6 4 1

  3. Ex 1) Expand (a + b)3 Look! Matches exponent!!

  4. Ex 2) Find the 13th term of the expansion (x + y)15 Look at 2nd variable: Starts with y0 y1 y2 y3 … So the 13th term would be 1 less: y12 Exponents add to 15 so exponent on x is 15 – 12 = 3: x3 Now the coefficient: exponent match exp. on x match exp. on y

  5. Ex 3) Find the 7th term in the expansion of (2x – y)10 2nd variable: exponent is 1 less than 7: (-y)6 1st variable: exponent is 10 – 6 = 4: (2x)4 Coeff: 7th term: 210 (2x)4 (-y)6 = 210(16x4)(y6) = 3360x4y6

  6. Ex 4) –35a8b3 is what term in (a2 – b)7 ? Look at 2nd variable starts with: b0 b1 b2 b3  4th term

  7. Ex 5) Find the middle term of (x2 + 2y)4 Look at 2nd variable (2y)0 (2y)1 (2y)2 (2y)3(2y)4 5 terms  middle = 3rd term (2y)2 Exp. on 2nd variable is 1 less than 3: (x2)2 Exp. on 1st variable is 4 – 2 = 2: Coeff: = 6 (x4) (4y2) = 24 x4y2

  8. Homework #1110 Pg. 542 1 – 23 odd (Don’t try this on the test!!!)

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