#1**0 **

Find the term not involving x for the expansion of (x^2-2y/x)^8

\((x^2-\frac{2y}{x})^8\\ \text{The nth term will be}\\ \binom{8}{n}(\frac{-2y}{x})^n(x^2)^{8-n}\\ =\binom{8}{n}(-2)^ny^n\frac{(x^2)^{8-n}}{x^n}\\ =\binom{8}{n}(-2)^ny^n x^{16-2n-n}\\ =\binom{8}{n}(-2)^ny^n x^{16-3n}\\\)

16-3n=0 has no integer solutions so there is no term that does not involve x.

Melody Aug 14, 2017