1. The problem is to prove a mathematical statement or theorem. Since the user did not specify which proof is needed, I will demonstrate a common algebraic proof: the distributive property $a(b+c) = ab + ac$. 2. The distributive property states that multiplying a number by a sum is the same as multiplying each addend separately and then adding the products. 3. Let $a$, $b$, and $c$ be any real numbers. We want to prove that: $$a(b+c) = ab + ac$$ 4. By definition of multiplication over addition, consider the left side: $$a(b+c)$$ 5. Using the property of addition inside the parentheses, we can write: $$a \times b + a \times c$$ 6. This is exactly the right side: $$ab + ac$$ 7. Therefore, the distributive property holds for all real numbers $a$, $b$, and $c$. This completes the proof.