Solving Binomial Expansions: Coefficient of x^k in (2x-1/x)^2007

[brunie]

Hi,
Im having some troubles with this binomial expansion...

Determine the coefficient of x^k, where k is any integer, in the expansion of (2x - 1/x)^2007.

I figured it would just be
C(2007,k) * (2x)^2007-k * (-1/x)^k
= C(2007,k) * (2)^2007-k * x^2007-k * (-1/x)^k

therefore the coefficient would only be the constant terms with no variables

but when i tried it on a smaller scale (ie small exponent), and factored it out, the equation i found doesn't work

i think it is due to the common variable x

anyone kno what to do?

 

[Dick]

x doesn't drop out of that expression. The power is x^(2007-2*k).

 

[brunie]

so
(2x)^2007-k isn't equivalent to (2)^2007-k * x^2007-k ??

 

[Dick]

Sure it is. But x^(2007-k)*(1/x)^k=x^(2007-2*k).

 

[brunie]

ok yes that makes sense
thanks for ur help