Are 2x and 3x^1 like terms?

Are 2x and 3x^1 like terms?

• A. Yes
• B. Only if coefficients equal
• C. No
• D. Only if exponents differ

Answer: (A)

Like terms have the same variable raised to the same exponent. Here both terms involve x to the first power, since x^1 equals x. The coefficients can be different (2 and 3) and that doesn’t affect whether they’re like terms. So 2x and 3x^1 are like terms and can be combined: 2x + 3x^1 = 5x. If the exponents differed, or if a different variable were present, they wouldn’t be like terms.

Like terms have the same variable raised to the same exponent. Here both terms involve x to the first power, since x^1 equals x. The coefficients can be different (2 and 3) and that doesn’t affect whether they’re like terms. So 2x and 3x^1 are like terms and can be combined: 2x + 3x^1 = 5x. If the exponents differed, or if a different variable were present, they wouldn’t be like terms.