jmc

Notice that if we add $x(x+y)$ and $y(x+y)$, we can factor out a term of $(x+y)$ to obtain $x(x+y)+y(x+y)=(x+y)(x+y)$. Thus, $(x+y{)}^2=x(x+y)+y(x+y)$, so $(x+y{)}^2=27+54=\boxed{81}$.