1 / 8

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:.

mackenzie-donaldson
Download Presentation

11.8 The General Binomial Expansion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!!!)

More Related