Step-by-step Solution:

Using the distributive law of Boolean algebra, which states that \(X \cdot (Y+Z) = (X \cdot Y) + (X \cdot Z)\), we can simplify the expression. Given expression: \(A \cdot (B+C)\) Applying the distributive law: \((A \cdot B) + (A \cdot C)\) or simply \(AB+AC\).