SOLUTION: The eighth term of the expansion (2c+d)^7 The first term of the expansion of (3q-7r)^6 The second term of the expansion of (a+3b)^10

Algebra ->  Sequences-and-series -> SOLUTION: The eighth term of the expansion (2c+d)^7 The first term of the expansion of (3q-7r)^6 The second term of the expansion of (a+3b)^10       Log On


   

Question 844870: The eighth term of the expansion (2c+d)^7
The first term of the expansion of (3q-7r)^6
The second term of the expansion of (a+3b)^10
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the kth term of 

(A + B)N  is

C(N,k-1)AN-k+1Bk-1

The eighth term of the expansion (2c+d)^7 

So substitute A = 2c, B = d, k = 8, N = 7


C(N,k-1)AN-k+1Bk-1
C(7,8-1)(2c)7-8+1d8-1
C(7,7)(2c)0d7
(1)(1)d7
d7

The first term of the expansion of (3q-7r)^6

So substitute A = 3q, B = -7r, k = 1, N = 6


C(N,k-1)AN-k+1Bk-1
C(6,1-1)(3q)6-1+1(-7r)1-1
C(6,0)(3q)6(-7r)0
(1)(3q)6(1)
(3q)6
36q6
729q6

Edwin