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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.

Omar Dennaoui
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Dan Stephens
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    Welcome to MSE. Please, use MathJax to type the math in your questions. Consider that many users in this forum won't even read your questions if they're not properly formatted, let alone help you. – jjagmath Mar 26 '24 at 17:04

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