$(10$ points$)$ Find the Boolean expressions.

$($a$)$ Convert $F=\frac{A}{b}ar(B)\frac{+}{b}ar(C)D$ to Product$-$of$-$Sums. $($Hint : use the Distributive Law.$)$

$($b$)$ Simplify $\frac{?}{\text{b}\text{a}\text{r}}((A+B+C))\frac{*}{b}ar(ABC)$ to expressions containing a minimum number of literals.