Are the terms 4x^2 and 4x like terms?

Are the terms 4x^2 and 4x like terms?

• A. Yes, they are like terms.
• B. No, they are not like terms.
• C. They can be combined.
• D. They have the same coefficient.

Answer: (B)

The correct understanding is that 4x^2 and 4x are not like terms because they have different variables and exponents. Like terms are defined as terms that contain the same variable raised to the same power. In this case, 4x^2 includes the variable x raised to the power of 2, while 4x has the variable x raised to the power of 1. Since the powers of the variable differ, these terms cannot be combined. Recognizing the distinction between the two types of terms is essential for proper algebraic simplification. Combining like terms involves only those that are of the same kind, ensuring that the variable factors and their exponents match. Therefore, it is clear why the terms 4x^2 and 4x do not qualify as like terms.

The correct understanding is that 4x^2 and 4x are not like terms because they have different variables and exponents. Like terms are defined as terms that contain the same variable raised to the same power. In this case, 4x^2 includes the variable x raised to the power of 2, while 4x has the variable x raised to the power of 1. Since the powers of the variable differ, these terms cannot be combined.

Recognizing the distinction between the two types of terms is essential for proper algebraic simplification. Combining like terms involves only those that are of the same kind, ensuring that the variable factors and their exponents match. Therefore, it is clear why the terms 4x^2 and 4x do not qualify as like terms.