What is an example of unlike terms?

• A. 3x and 5x
• B. 5x and 7y
• C. 2a and 2b
• D. 4xy and 4x^2

Answer: (B)

Unlike terms are terms that have different variable parts, meaning they cannot be combined through addition or subtraction because they represent different quantities. In the provided options, the terms that demonstrate this characteristic must have either different variables or different variable exponents.

The correct answer illustrates unlike terms because 5x and 7y involve two distinct variables, x and y. This means that they cannot be combined in any algebraic expression, as they represent different dimensions or categories of quantities.

Considering the other examples: 3x and 5x are like terms because they share the same variable (x), allowing them to be combined. Similarly, 2a and 2b also belong to different categories (a and b), making them unlike terms but not the most fitting comparison in the context; whereas 4xy and 4x^2 involve the same variable, x, but in different forms (one has a y term while the other has a square), they are effectively unlike terms as well. However, the strongest and most straightforward example of unlike terms is the one with the variables x and y, as they present the most direct distinction.