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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 )

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Today in Precalculus

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  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

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