Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the significance of the distributive property in algebra?

1. It helps you factor equations

2. It allows us to multiply a single term by two or more terms inside parentheses

3. It defines the structure of algebraic equations

4. It simplifies cubic equations

The correct answer is: It allows us to multiply a single term by two or more terms inside parentheses

The significance of the distributive property in algebra primarily lies in its ability to facilitate the multiplication of a single term by two or more terms within parentheses. This property states that when you multiply a number (or term) by a sum, you can distribute that number across the terms being summed. For example, if you have \( a(b + c) \), the distributive property allows you to rewrite it as \( ab + ac \). This operation simplifies expressions and is foundational for simplifying equations, solving problems, and expanding polynomials, making it a crucial concept in algebra. Options discussing factoring, the definition of algebraic structures, or simplifying cubic equations, while they may relate to broader concepts in algebra, do not specifically highlight the core function of the distributive property itself. The property is specifically designed for handling multiplication in relation to addition or subtraction within expressions, which directly correlates to the option about multiplying a single term by multiple terms inside parentheses.