Suppose Alive and Bob have shares of two polynomials $P,Q$, say, Alice knows $P_A,Q_A$, Bob knows $P_B,Q_B$ s.t. $P=P_A+P_B$ and $Q=Q_A+Q_B$. They perform some operation $f$ over the shared values, to obtain shares of $f(P,Q)$.
If they reveal the shares of $f(P,Q)$, will this give hints on their individual shares of $P,Q$?
I am supposing that one cannot deduce $P$ or $Q$ with the knowledge of $f(P,Q)$. I just want Alice and Bob to know $f(P,Q)$ without leaking shares.