Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What does "simplifying an expression" involve?

1. Finding the greatest common factor of the expression

2. Reducing the expression to its simplest form while maintaining equivalence

3. Changing the expression into a polynomial

4. Breaking down the expression into its factors

The correct answer is: Reducing the expression to its simplest form while maintaining equivalence

Simplifying an expression involves reducing it to its simplest form while maintaining equivalence. This process aims to make the expression easier to read, work with, and understand, often involving operations such as combining like terms, reducing fractions, or eliminating unnecessary parentheses. The goal is to express the same value in a more straightforward, compact manner. For example, simplifying \(2x + 3x\) involves combining like terms to yield \(5x\). The expression is still equivalent to the original, but it is presented in a simpler form. In contrast, while finding the greatest common factor, changing an expression into a polynomial, or breaking down the expression into its factors are valid mathematical operations, they do not specifically capture the essence of simplifying an expression as described. They may be steps within the simplification process or related concepts, but the core idea of simplification itself is to present the expression in its most straightforward and understandable form without changing its value.