Are 3x and 3x^2 like terms?

• A. Yes, they are like terms
• B. No, they are not like terms
• C. They become like terms when added
• D. Only if coefficients are identical

Answer: (B)

To understand why 3x and 3x^2 are not like terms, it’s important to recognize what constitutes like terms in algebra. Like terms are terms that have the exact same variable raised to the same power. In this case, 3x contains the variable x raised to the power of 1, while 3x^2 contains the variable x raised to the power of 2. Since the powers of the variable differ (1 in the first term and 2 in the second), these terms cannot be combined through addition or subtraction.

When simplifying algebraic expressions, combining like terms allows you to consolidate the expression into fewer terms, reducing complexity. However, since 3x and 3x^2 represent different dimensions or characteristics (specifically due to the exponent), they cannot be combined.

This understanding of like terms is fundamental when simplifying algebraic equations, as it underpins many operations performed in algebra. Recognizing that terms with different variable exponents are distinct ensures clarity in simplification processes.