# Expanding this boolean expression

Can this Boolean expression:

$$A*\overline{A*B}$$

be expanded to give:

$$A*\overline{A} * A*\overline{B}$$

Although that appears to reduce to zero?

I know $A(\overline{A+B})$ can be expanded to give: $A*A + A*\overline{B}$

So can it work with an AND? How else do you simplify the first expression?

-
To put it over multiple characters, you can use \overline{} instead of \bar{}: $w+\overline{x+y}+z$. –  Michael Hardy Jan 5 '12 at 3:05
A more general comment: If you work with small boolean expressions (<4 variables) a truth-table for both expressions can always determine equivalence. –  chazisop Jan 5 '12 at 16:20

No. By De Morgan's laws, $$(A * B)' = A' + B'.$$ So, $A*(A*B)'$ can be expanded to give $$A*(A'+B') = A*A' + A*B' = \mathsf{F} + A*B' = A*B'.$$