What does it mean to combine like terms in an algebraic expression?

• A. Simplifying an expression by factoring
• B. Removing all variable terms from the expression
• C. Adding or subtracting terms with the same variable and power
• D. Grouping all terms with different variables together

Answer: (C)

When we talk about combining like terms in an algebraic expression, we focus on adding or subtracting terms that share the same variable and have the same exponent. This process is essential for simplifying expressions because it consolidates the various terms into a more manageable form.

For example, in the expression (3x + 5x), both terms contain the same variable (x) with the same power of 1. By adding them together, we get (8x). Similarly, if we look at (4y^2 - 2y^2), the terms can be combined to yield (2y^2) since they both contain the variable (y) raised to the second power.

The correct answer emphasizes that only terms with matching variables and exponents can be combined, which is a fundamental rule in algebraic simplification. Understanding this principle is crucial for effectively manipulating and simplifying algebraic expressions, making option C the right choice.

In contrast, the other options describe incorrect or irrelevant concepts regarding combining like terms. For instance, factoring, removing variables, or grouping terms with different variables do not align with the definition or the process of combining like terms.