FTCE Professional Education Practice Exam

How can the distributive property be expressed mathematically?

1. a + (b + c) = ab + ac

2. a (b + c) = ab + ac

3. a (b + c) = a + b + c

4. (a + b)c = ac + bc

The correct answer is: a (b + c) = ab + ac

The distributive property is a fundamental principle in mathematics that describes how to multiply a single term by a sum or difference of terms. When using the distributive property, you can express the multiplication of a term with a group of terms inside parentheses. The correct expression of the distributive property is represented by stating that multiplying a number (or variable) by a sum involves distributing that number across each term inside the parentheses. This can be formulated mathematically as a multiplied by (b plus c), which equals the product of a and b plus the product of a and c. Thus, when you see the expression a(b + c) = ab + ac, it illustrates that a is multiplied separately by both b and c, resulting in the sum of those two products. This forms the core of the distributive property, demonstrating that multiplication distributes over addition. The other choices either misrepresent how the distributive property is applied or present incorrect mathematical relationships. Understanding this concept is key in solving equations and simplifying expressions effectively in algebra.