jmc

If we expand the left hand side of the first equation, we get $x^2+2xy+y^2=105$, so $2xy+(x^2+y^2)=105$. We are given that $x^2+y^2=65$, so we can substitute for $x^2+y^2$ to obtain $2xy+65=105$. It follows that $xy=\boxed{20}$.