\[y(y + 3)^{2} - y^{2}(y + 3) =\]
\[= (y + 3)\left( y(y + 3) - y^{2} \right) =\]
\[= (y + 3)\left( y^{2} + 3y - y^{2} \right) =\]
\[= 3y(y + 3)\]