True or False: The terms 4xy and 4x²y can be combined.

True or False: The terms 4xy and 4x²y can be combined.

• A. True
• B. False
• C. Depends on the context
• D. Only if they have the same coefficient

Answer: (B)

To determine whether the terms 4xy and 4x²y can be combined, it is essential to understand what "like terms" are. Like terms are terms that contain the same variable factors raised to the same powers. In this case, 4xy has the variables x and y, while 4x²y includes x raised to the second power (x²) and y. Although both terms share the variable y, they differ in how the variable x is represented. The power of x is crucial here: in 4xy, x is to the first power, while in 4x²y, x is squared. Since the powers of x are different in the two terms, they are not considered like terms and therefore cannot be combined. When combining like terms, only those with identical variable parts can be combined, regardless of their coefficients. Thus, it is accurate to state that the statement regarding the ability to combine 4xy and 4x²y is false.

To determine whether the terms 4xy and 4x²y can be combined, it is essential to understand what "like terms" are. Like terms are terms that contain the same variable factors raised to the same powers.

In this case, 4xy has the variables x and y, while 4x²y includes x raised to the second power (x²) and y. Although both terms share the variable y, they differ in how the variable x is represented. The power of x is crucial here: in 4xy, x is to the first power, while in 4x²y, x is squared.

Since the powers of x are different in the two terms, they are not considered like terms and therefore cannot be combined. When combining like terms, only those with identical variable parts can be combined, regardless of their coefficients.

Thus, it is accurate to state that the statement regarding the ability to combine 4xy and 4x²y is false.