True or False: You can combine 2ab and 3a²b together.

• A. True
• B. False
• C. Only if a = 1
• D. Only if b = 1

Answer: (B)

To determine whether you can combine the terms 2ab and 3a²b, it's important to understand the concept of like terms in algebra. Like terms are terms that contain the same variables raised to the same powers. In this case, 2ab and 3a²b involve the variables 'a' and 'b', but they are not like terms because their variable components differ in their powers.

2ab has 'a' raised to the first power and 'b' also raised to the first power, while 3a²b has 'a' raised to the second power and 'b' raised to the first power. Since the power of 'a' is different between the two terms—one term has 'a' to the power of 1 and the other has 'a' to the power of 2—they cannot be combined through addition or subtraction. Therefore, the statement that you can combine these two terms is false.

This reasoning shows why the determination of "False" is correct: the key to combining terms is that they must match in variable type and exponent. Since these conditions are not met here, the terms remain separate in any algebraic expression.