Simplifying the Boolean expression $A + \bar{A}\bar{B}$?
There is a Law of Distributivity of Boolean operation $\lor$ (disjunction, which is sometimes denoted by $+$) over Boolean operation $\land$ (conjunction, which is sometimes simply omitted):
$$x \lor (y \land z)= (x \lor y)\land(x \lor z)$$
So, in your case:
$$A \lor (\lnot A \land \lnot B) = (A \lor \lnot A) \land (A \lor \lnot B) = A \lor \lnot B$$
For more information please see: Boolean Algebra.