time complexity - How do i add 2 Big O notations

Question

I have algorithm one that has a complexity of O(mnr +mr^2 + nr^2 ) + K x (mr^2 + nr^2)

and the second algorithm which is Estep = Q.X + (1-Q).(W*H) which i computed as O(mnr)

where (.) is element-wise multiplication

Now i want to add O(mnr) to O(mnr) +mr^2 + nr^2 + K x (mr^2 + nr^2)

Question:

1. do you agree with my complexity of the second statement?
2. what will be the final complexity

Thanks for your time

Answer 1

You can simplify O(mnr) + O(mnr +mr^2 + nr^2) + K x (mr^2 + nr^2) as O(mnr + mr^2 + nr^2). You cannot simplify further without any assumption on the relationship between m, n and r.