I am sorry if I wasn't clear.
I read the updated answer and I have changed the question a bit in response to your comment that "If either k or m is a variable then the equality (n+k)m = Θ(nm) does not hold".
So if n, m are variables and only k is constant, then what will be the relation?
Now we can't ignore the mcr term that will come in expansion of (n+k)m as 'm' is a variable.
For this case I have calculated, (n+k)m = O(mm/2. nm+1 ) as the answer.
Is my method and/or answer correct for this particular case?
P.S. Sometimes I feel I am asking for quite valuable from you guys and I don't feel comfortable about it. You and others are already doing so much for this amazing platform.