Suppose that the functions $r$ and $s$ are defined for all real numbers $x$ as follows.
\[
\begin{array}{l}
r(x)=x^{3} \\
s(x)=3 x^{2}
\end{array}
\]
Write the expressions for $(s+r)(x)$ and $(s-r)(x)$ and evaluate $(s \cdot r)(-2)$.

Step 1 ：Let the functions $r$ and $s$ be defined as $r(x)=x^{3}$ and $s(x)=3 x^{2}$ for all real numbers $x$.

Step 2 ：To find the expression for $(s+r)(x)$, we add the expressions for $s(x)$ and $r(x)$ together to get $x^{3} + 3x^{2}$.

Step 3 ：To find the expression for $(s-r)(x)$, we subtract the expression for $r(x)$ from the expression for $s(x)$ to get $-x^{3} + 3x^{2}$.

Step 4 ：To evaluate $(s \cdot r)(-2)$, we multiply the expressions for $s(-2)$ and $r(-2)$ together to get $-96$.

Step 5 ：Thus, the expressions for $(s+r)(x)$ and $(s-r)(x)$ are \(\boxed{x^{3} + 3x^{2}}\) and \(\boxed{-x^{3} + 3x^{2}}\) respectively. The value of $(s \cdot r)(-2)$ is \(\boxed{-96}\).