How to simplify Boolean Expression $\bar B + \bar C (B + A)$ I trying to figure out how $ \bar B + \bar C (B + A)$ simplifies to 
$ \bar B + \bar C$.

It's usually easier to figure these things out with Karnaugh maps. After playing around, we see that:
\begin{align*}
\overline B + \overline C(B + A)
&= \overline B(1) + \overline C(B + A) \\
&= \overline B(1 + \overline C) + \overline C(B + A) \\
&= \overline B + \overline B ~ \overline C + \overline C(B + A) \\
&= \overline B + \overline C(\overline B + B + A) \\
&= \overline B + \overline C(1 + A) \\
&= \overline B + \overline C(1) \\
&= \overline B + \overline C
\end{align*}
as desired.
