a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c)
This resembles the distributive law in numerical algebra. However, the following is also true in Boolean algebra.
a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c)
Each distributive law can be proven by enumerating all eight possible combinations of values for a, b and c, and show that both sides of the equality are indeed the same.