Which law is represented by a(b+c) = ab + ac?

Which law is represented by a(b+c) = ab + ac?

• A. Commutative Law for Addition
• B. Associative Law for Addition
• C. Distributive Law
• D. Identity Law for Addition

Answer: (C)

The equation a(b+c) = ab + ac represents the Distributive Law. This law states that when a term is multiplied by a sum, it can be distributed to each addend within the parentheses. In this case, a is distributed to both b and c. The left side, a(b+c), emphasizes that you can take a single term (a) and multiply it by a combined term (b+c) as if you were multiplying each individual part separately. The right side, ab + ac, clearly shows the result of this distribution—where a is multiplied by b and then separately by c. Recognizing the Distributive Law is crucial for simplifying algebraic expressions and solving equations, as it allows you to break down complex problems into more manageable parts. This understanding is essential in many mathematical applications and often serves as a foundational concept for more advanced topics.

The equation a(b+c) = ab + ac represents the Distributive Law. This law states that when a term is multiplied by a sum, it can be distributed to each addend within the parentheses.

In this case, a is distributed to both b and c. The left side, a(b+c), emphasizes that you can take a single term (a) and multiply it by a combined term (b+c) as if you were multiplying each individual part separately. The right side, ab + ac, clearly shows the result of this distribution—where a is multiplied by b and then separately by c.

Recognizing the Distributive Law is crucial for simplifying algebraic expressions and solving equations, as it allows you to break down complex problems into more manageable parts. This understanding is essential in many mathematical applications and often serves as a foundational concept for more advanced topics.