What is the constant in this Binomial? Full Explanation!

(3/X - X^3)^8 Ive tried it like 10 tens and can't get it!! Thanks!

The constant would be the term where, after expanding the binomial, the X terms cancelled.
Since the Yth (starting from 0) term is 8CY * (3/X) ^ (8-Y) * (-X^3) ^ Y, that simplifies to:
8CY * (3/X)^(8-Y) * (- X)^3Y
And the Xs will cancel when 8-Y = 3Y
8 = 4Y
Y = 2

Substitute for Y=2:
8C2 * (3/X)^(8-2) * (-X)^(3*2)
= 28 * (3/X)^6 * (-X)^6
= 28*3^6
= 28 * 729
= 20,412

I can only think that by the 'constant' you mean the term in the expansion which is independent of x. For the binomial

f(x) = (3/x - x³)^8

the kth term is given by 8Ck.(3/x)^(8-k).(-x³)^k

and for the power of x to be zero requires that -(8 - k) + 3.k = 0, or k = 2.

This term then takes the form 8C2.(3/x)^6.(-x³)² = [8*7/2!].3^6.(-1)² = 20412.

I would assume its the ^8 at the end because its the only value that inst a coefficient or Variable.