Here are my questions:
Simplify the following $O$-notation statements as much as possible, e.g. $O(n + 25 + \log(2n)) = O(n)$.
(i) $O(n^2 + n)$
(ii) $O(\log(2n)) + O(n) + O(n^2)$
(iii) $O(n) * O(\log(2n)) $
(iv) $O(2^n) * O(n^2 + 2^n + \log(2n))$
I know the first three answers are:
(i) $O(n^2)$
(ii) $O(n^2)$
(iii) $O(n\log(2n))$
However, I'm unsure on the last one. Would it be $O(2^n)$ or would it be whatever $O(2^n) * O(2^N)$ is, which I'm not even sure what that is? How do you simplify Big $O$ notations with multiplication involved.
Many thanks if anyone can help.