problem: Expand the following product: $\frac{1}{4}\left(\frac{4}{y} + 4y\right)$.
solution: We apply the distributive property to get\begin{align*}
  \frac{1}{4}\left(\frac{4}{y}+4y\right)&= \frac{1}{4}\cdot\frac{4}{y}+\frac{1}{4}\cdot 4y\\
  &= \boxed{\frac{1}{y} + y}.
  \end{align*}