Are the terms 5ab and 5a^2b considered equivalent or unlike terms?

Are the terms 5ab and 5a^2b considered equivalent or unlike terms?

• A. Equivalent terms
• B. Unlike terms
• C. Identical terms
• D. Similar terms

Answer: (B)

The terms 5ab and 5a^2b are classified as unlike terms because they have different variable structures. To break it down, both terms have the coefficient 5, but the exponents of the variables differ. The term 5ab consists of a single 'a' raised to the first power (a^1) and a 'b' raised to the first power (b^1). In contrast, the term 5a^2b contains 'a' raised to the second power (a^2) while 'b' remains at the first power. When combining like terms, we need to look for terms that have exactly the same variable factors raised to the same exponents. In this scenario, since the presence of 'a' has different exponents between the two terms, they cannot be combined or simplified together, making them unlike terms. This is why the classification as unlike terms is accurate.

The terms 5ab and 5a^2b are classified as unlike terms because they have different variable structures.

To break it down, both terms have the coefficient 5, but the exponents of the variables differ. The term 5ab consists of a single 'a' raised to the first power (a^1) and a 'b' raised to the first power (b^1). In contrast, the term 5a^2b contains 'a' raised to the second power (a^2) while 'b' remains at the first power.

When combining like terms, we need to look for terms that have exactly the same variable factors raised to the same exponents. In this scenario, since the presence of 'a' has different exponents between the two terms, they cannot be combined or simplified together, making them unlike terms. This is why the classification as unlike terms is accurate.