SOLUTION: Find the coefficient of the term x球⁶ in the binomial expansion of the expression (3x - 2y)⁸ A.) 81,648 B.) 16,128 C.) -81,648 D.) -16,128

Algebra ->  Permutations -> SOLUTION: Find the coefficient of the term x球⁶ in the binomial expansion of the expression (3x - 2y)⁸ A.) 81,648 B.) 16,128 C.) -81,648 D.) -16,128      Log On


   



Question 1081387: Find the coefficient of the term x球⁶ in the binomial
expansion of the expression (3x - 2y)⁸
A.) 81,648
B.) 16,128
C.) -81,648
D.) -16,128

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find the coefficient of the term x球⁶ in the binomial
expansion of the expression (3x - 2y)⁸
%28a%2Bb%29%5En%22%22=%22%22sum%28nCk%2Aa%5E%28n-k%29b%5Ek%2Ck=0%2Cmatrix%281%2C4%2C%22%22%2C%22%22%2Cn%2C%22%22%29%29

For the term in x%5E2y%5E6, a=3x, b=-2y,  n=8,  k=6, n-k=8-6=2

nCk%2Aa%5E%28n-k%29b%5Ek%22%22=%22%228C2%2A%283x%29%5E2%28-2y%29%5E6%22%22=%22%2228%2A3%5E2x%5E2%2A%28-2%29%5E6y%5E6%22%22=%22%2228%2A9x%5E2%2A%2864%29y%5E6%22%22=%22%2216128x%5E2y%5E6

Edwin