What does the distributive property allow you to do?

What does the distributive property allow you to do?

• A. Add two coefficients together
• B. Multiply a number by each term within parentheses
• C. Switch the order of addition
• D. Assign values to variables

Answer: (B)

The distributive property is a fundamental principle in mathematics that relates to how multiplication interacts with addition. It states that when you multiply a number by a sum of terms, you can distribute the multiplication across each term inside the parentheses. This means that if you have an expression such as \(a(b + c)\), according to the distributive property, you can rewrite it as \(ab + ac\). This property helps simplify algebraic expressions and facilitates computations, making it easier to solve equations and evaluate expressions. It is especially useful in expanding expressions and performing operations efficiently. The other options describe different mathematical concepts. Adding coefficients is a straightforward arithmetic operation, switching the order of addition refers to the commutative property, and assigning values to variables is part of the process of solving equations or evaluating expressions, but it doesn't directly relate to the distributive property itself.

The distributive property is a fundamental principle in mathematics that relates to how multiplication interacts with addition. It states that when you multiply a number by a sum of terms, you can distribute the multiplication across each term inside the parentheses. This means that if you have an expression such as (a(b + c)), according to the distributive property, you can rewrite it as (ab + ac).

This property helps simplify algebraic expressions and facilitates computations, making it easier to solve equations and evaluate expressions. It is especially useful in expanding expressions and performing operations efficiently.

The other options describe different mathematical concepts. Adding coefficients is a straightforward arithmetic operation, switching the order of addition refers to the commutative property, and assigning values to variables is part of the process of solving equations or evaluating expressions, but it doesn't directly relate to the distributive property itself.