What does the distributive property state?

What does the distributive property state?

• A. a(b + c) = ab + ac
• B. ab + ac = a(b + c)
• C. a(b - c) = ab - ac
• D. (a + b)c = ac + bc

Answer: (A)

The distributive property states that when you multiply a number by a sum, you can distribute the multiplication to each addend in the sum. Specifically, it asserts that if you have a number \( a \) multiplied by the sum of \( b \) and \( c \), the expression can be rewritten as the sum of two products: \( a \) times \( b \) and \( a \) times \( c \). This mathematically appears as \( a(b + c) = ab + ac \), confirming that you apply the multiplication to each component inside the parentheses. This property is fundamental in algebra and ensures that expressions are managed consistently when simplifying or solving equations. While other options also present valid mathematical relationships, they either represent variations or alternative expressions of the distributive property that do not capture its primary statement in the form most commonly referred to. This highlights the importance of recognizing the distributive property correctly as it serves as a foundational concept for further mathematical operations.

The distributive property states that when you multiply a number by a sum, you can distribute the multiplication to each addend in the sum. Specifically, it asserts that if you have a number ( a ) multiplied by the sum of ( b ) and ( c ), the expression can be rewritten as the sum of two products: ( a ) times ( b ) and ( a ) times ( c ).

This mathematically appears as ( a(b + c) = ab + ac ), confirming that you apply the multiplication to each component inside the parentheses. This property is fundamental in algebra and ensures that expressions are managed consistently when simplifying or solving equations.

While other options also present valid mathematical relationships, they either represent variations or alternative expressions of the distributive property that do not capture its primary statement in the form most commonly referred to. This highlights the importance of recognizing the distributive property correctly as it serves as a foundational concept for further mathematical operations.