SOLUTION: Find the term that is independent of x in the expansion of {{{ (2 + 3/x^2) (x - 2/x)^6 }}}.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the term that is independent of x in the expansion of {{{ (2 + 3/x^2) (x - 2/x)^6 }}}.       Log On


   

Question 1187212: Find the term that is independent of x in the expansion of +%282+%2B+3%2Fx%5E2%29+%28x+-+2%2Fx%29%5E6+.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Expanded, %28x+-+2%2Fx%29%5E6+ is a polynomial with 7 terms.
It has terms in X%5E6 , x%5E4 , x%5E2, x%5E0 (an independent term), x%5E%28-2%29, x%5E%28-4%29, y x%5E%28-6%29 .
The independent term in that polynomial is
20%28x%5E3%29%28-2%2Fx%29%5E3=20%28-2%29%5E3=20%28-8%29=-160 .
The term in x%5E2 in that polynomial is 15%28x%5E4%29%28-2%2Fx%29%5E2=15%284%29x%5E2=60x%5E2
The independent term in the product +%282+%2B+3%2Fx%5E2%29+%28x+-+2%2Fx%29%5E6+ would be
2%28-160%29%2B%283%2Fx%5E2%29%2860x%5E2%29=-320%2B3%2860%29=-320%2B180=-140