Big O time complexity simplification

Question

Is it ok to say that the time complexity of the order O((p+1)(v^2)) is equal to O(p(v^2))? p and v are sizes of the inputs.

Here is the problem: O(v^2) + O(p*(v^2))

And here is my answer: = O((p+1)(v^2)) =? O(p(v^2))

Answer 1

Yes that is correct as long as p is asymptotically bounded by a positive constant from below, which is particularly the case if p is increasing non-negative function in the context of the limit under consideration (i.e. the input size).