SOLUTION: Find the first three terms in the expansion, in descending powers of x, of (x- 2/x)^6. find the coefficient of x^4 in the expansion of (2+3x^2)(x-2/x)^6

Algebra ->  Statistics  -> Binomial-probability -> SOLUTION: Find the first three terms in the expansion, in descending powers of x, of (x- 2/x)^6. find the coefficient of x^4 in the expansion of (2+3x^2)(x-2/x)^6      Log On


   



Question 1117629: Find the first three terms in the expansion, in descending powers of x, of (x- 2/x)^6. find the coefficient of x^4 in the expansion of (2+3x^2)(x-2/x)^6
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


%28x-2%2Fx%29%5E6 =
x%5E6+%2B+6%2A%28x%29%5E5%2A%28-2%2Fx%29%5E1+%2B+15%2A%28x%29%5E4%2A%28-2%2Fx%29%5E2 plus other terms.... =

x%5E6-12x%5E4%2B60x%5E2 plus other terms....

The coefficient of x^4 in the expansion of

%282%2B3x%5E2%29%2A%28x%5E6-12x%5E4%2B60x%5E2%29

is

%282%29%28-12%29%2B3%2860%29+=+-24%2B180+=+156