True or False: You can combine 2xy and 4yx.

• A. True
• B. False
• C. Only if grouped together
• D. Only if they have the same coefficient

Answer: (A)

The statement is true because 2xy and 4yx represent the same term. In algebra, terms are considered "like terms" when they have the same variables raised to the same powers, regardless of the order in which those variables appear. Both 2xy and 4yx can be arranged in the same format because multiplication is commutative; thus, 2xy is equivalent to 2yx and 4yx is equivalent to 4xy.

Combining like terms involves adding or subtracting the coefficients while keeping the variable parts the same. Therefore, if you were to combine 2xy and 4yx, you would add the coefficients (2 and 4) to get a total coefficient of 6, resulting in 6xy (or equivalently 6yx). This confirms that they can indeed be combined since they are like terms.