Which set of terms can be combined: 5a^2, 6a^2, and 2a?

• A. 5a^2 and 6a^2
• B. 6a and 2a
• C. 5a and 6a
• D. None of these can be combined

Answer: (A)

The correct choice is based on the principle of combining like terms. In algebra, like terms are terms that have the same variable raised to the same exponent.

In the given set of terms, 5a² and 6a² are both quadratic terms because they contain the variable 'a' raised to the power of 2. These two terms can be combined because they share the same variable and exponent. When you combine them, the coefficients (the numbers in front) are added together:

5a² + 6a² = (5 + 6)a² = 11a².

However, the term 2a cannot be combined with either 5a² or 6a² because it is a linear term, not a quadratic term. Therefore, 2a does not match the criteria to be combined with the other two terms.

This reasoning highlights why the selection of 5a² and 6a² is indeed the appropriate answer.