Which of the following expressions contains unlike terms?

Which of the following expressions contains unlike terms?

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

Answer: (D)

The expression that contains unlike terms is indeed the one where 7z and 7z^2 are part of the selection. To understand why this is the case, we need to look closely at the definitions and characteristics of like and unlike terms. Like terms are terms that have exactly the same variable factors raised to the same powers. In contrast, unlike terms have different variable factors or different powers of the same variable. In the case of 7z and 7z^2, we note that the first term has a variable z raised to the first power, while the second term has z raised to the second power. Because these two terms do not share the same exponent for the variable z, they are considered unlike terms. In comparison, the other pairs of terms provided show similarities that classify them as like terms. For instance, 4xy and 2xy have the same variables and the same exponent on each. Similarly, 5a and 5b both involve different variables but share the same coefficient structure, which does not affect their classification under the rules of combining like terms. Lastly, 3x^2 and 3xy, although they have a common coefficient, involve different variable arrangements and thus are also classified as unlike

The expression that contains unlike terms is indeed the one where 7z and 7z^2 are part of the selection. To understand why this is the case, we need to look closely at the definitions and characteristics of like and unlike terms.

Like terms are terms that have exactly the same variable factors raised to the same powers. In contrast, unlike terms have different variable factors or different powers of the same variable.

In the case of 7z and 7z^2, we note that the first term has a variable z raised to the first power, while the second term has z raised to the second power. Because these two terms do not share the same exponent for the variable z, they are considered unlike terms.

In comparison, the other pairs of terms provided show similarities that classify them as like terms. For instance, 4xy and 2xy have the same variables and the same exponent on each. Similarly, 5a and 5b both involve different variables but share the same coefficient structure, which does not affect their classification under the rules of combining like terms. Lastly, 3x^2 and 3xy, although they have a common coefficient, involve different variable arrangements and thus are also classified as unlike