Boolean Algebra Question (Logic Circuits)
$$(A + B) \cdot (A + C) $$
Distributive.  Multiply out terms.
$$ AA + AC + BA + BC $$
Idempotent
$$ A + AC + BA + BC $$
Distributive again.  Seek common factors.
$$ A (1 + C + B) + BC $$
Annulment
$$ A + BC $$
Laws and Theorems of Boolean Algebra