Which of the following pairs are like terms?

• A. 5a and 5b
• B. 3x² and 4x
• C. 2y and 3y
• D. 6xy and x²y

Answer: (C)

Like terms are terms that have the same variable raised to the same power, allowing them to be combined through addition or subtraction. In this case, when examining the pairs:

The pair consisting of 2y and 3y are like terms because they both contain the variable y with the same exponent of 1 (which is often implied and not written). This means they can be combined, resulting in the sum of their coefficients. If you were to combine them, it would yield 5y.

In contrast, the other pairs do not share this characteristic. For instance, while 5a and 5b both contain coefficients, they involve different variables, thus they are not like terms. Similarly, 3x² and 4x involve different powers of x—x² versus x—making them unlike as well. Lastly, 6xy and x²y have different forms in terms of their variable composition, since one term has the variable y combined with x while the other has a different exponent for x, preventing them from being categorized as like terms.

Understanding that like terms must share the same variable and exponent is key to simplifying algebraic expressions effectively.