Bc1 with the idea to play Nb2 perhaps?
Edit: Actually I can't see anything wrong with QxQ followed by Nc5 either. Hopefully someone can point the solution(s?) out.
Edit2: Ok there's Nb3 to block mate for the second one.
New player - Help needed with thought process
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oh, ok, qxq and wherever the knight goes Nc5 or q a6 is mate
After QXQ Nc4 Qa6+ black can put the knight in the way. In that various white has to play Nc5 mate.
I have edited it