after multiplying and simplifying (1-u)(2u+1/3) I get 2u+1/3-2u^2-1/3u but im unsure if im correct could anyone tell us if this is correct?
What I am sure you intended to write is correct. But most people would interpret "2u+1/3-2u^2-1/3u" as "2u+ 1/3- 2u^2- 1/(3u)" which is incorrect.
What you intended was, I think, "2u+ 1/3- 2u^2- (1/3)u" or, perhaps better, "2u+ 1/3- 2u^2- u/3". Those are correct.