True or False: The terms 6ab and 7a²b can be combined.

True or False: The terms 6ab and 7a²b can be combined.

• A. True
• B. False
• C. Only if exponent is ignored
• D. Only if coefficients are the same

Answer: (B)

In order to combine like terms in algebra, the terms must have identical variables raised to the same powers. The term "6ab" consists of a coefficient of 6, a variable 'a' raised to the first power, and a variable 'b' also raised to the first power. On the other hand, "7a²b" consists of a coefficient of 7, a variable 'a' raised to the second power, and a variable 'b' raised to the first power. These terms cannot be combined because the exponent on 'a' differs; one term has 'a' to the first power while the other has 'a' squared. Since they are not the same in terms of variable structure, they are considered different terms. As a result, the statement is false. This reasoning clarifies that to combine terms, they must share the same base variables raised to matching exponents, which is not the case here. Thus, the identification of the answer as false reflects an understanding of the rules governing algebraic expressions and simplifying them.

In order to combine like terms in algebra, the terms must have identical variables raised to the same powers. The term "6ab" consists of a coefficient of 6, a variable 'a' raised to the first power, and a variable 'b' also raised to the first power. On the other hand, "7a²b" consists of a coefficient of 7, a variable 'a' raised to the second power, and a variable 'b' raised to the first power.

These terms cannot be combined because the exponent on 'a' differs; one term has 'a' to the first power while the other has 'a' squared. Since they are not the same in terms of variable structure, they are considered different terms. As a result, the statement is false.

This reasoning clarifies that to combine terms, they must share the same base variables raised to matching exponents, which is not the case here. Thus, the identification of the answer as false reflects an understanding of the rules governing algebraic expressions and simplifying them.