1 / 7

Today in Precalculus

Today in Precalculus. Binomial Theorem Finding specific terms in a polynomial expansion homework. (2x 2 + 3y) 4 = 4 C 0 (2x 2 ) 4 (3y) 0 4 C 1 (2x 2 ) 3 (3y) 1 4 C 2 (2x 2 ) 2 (3y) 2 4 C 3 (2x 2 ) 1 (3y) 3 4 C 4 (2x 2 ) 1 (3y) 4. =(1)16x 8 (1) =4(8x 6 )(3y) =6(4x 4 )(9y 2 )

honorato-joyner
Download Presentation

Today in Precalculus

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. Today in Precalculus • Binomial Theorem • Finding specific terms in a polynomial expansion • homework

  2. (2x2 + 3y)4 = 4C0(2x2)4(3y)0 4C1(2x2)3(3y)1 4C2(2x2)2(3y)2 4C3(2x2)1(3y)3 4C4(2x2)1(3y)4 =(1)16x8(1) =4(8x6)(3y) =6(4x4)(9y2) =4(2x2)(27y3) =(1)(1)(81y4) Using Binomial Theorem 16x8+ 96x6y + 216x4y2 + 216x2y3 + 81y4

  3. (x – y2)5 = 5C0(x)5(-y2)0 5C1(x)4(-y2)1 5C2(x)3(-y2)2 5C3(x)2(-y2)3 5C4(x)1(-y2)4 5C5(x)0(-y2)5 =1(x5)(1) =5x4(-y2) =10(x3)(y4) =10(x2)(-y6) =5(x)(y8) =(1)(1)(- y10) Using Binomial Theorem x5 - 5x4y2 + 10x3y4 - 10x2y6 + 5xy8- y10

  4. Finding Specific Terms Find the x6y5 term in the expansion of (x + 3y)11 11C5(x)6(3y)5 = 462x6(243y5) =112,266x6y5

  5. Finding Specific Terms Find the x4y9 term in the expansion of (x - 2y)13 13C9(x)4(-2y)9 =715x4(-512)y9 =-366,080x4y9

  6. Homework • Pg 715:2,4,14,16,22,24

  7. Binomial Theorem (a + b)n = nC0an + nC1an-1b + nC2an-2b2 + … + nCn-2a2bn-2 + nCn-1abn-1 + nCnbn Note: nCr can also be written as

More Related