Which expression represents the sum of like terms 2a + 3a + 4b + 5b?

• A. 5a + 9b
• B. 2a + 3b
• C. 7a + 4b
• D. 6a + 7b

Answer: (A)

To find the expression that represents the sum of like terms in the expression 2a + 3a + 4b + 5b, we need to combine the coefficients of the like terms separately.

Starting with the 'a' terms, we have 2a and 3a. When you combine these, you add the coefficients:

2 (the coefficient of the first term) + 3 (the coefficient of the second term) equals 5. So, when combined, the 'a' terms result in 5a.

Next, we analyze the 'b' terms, which are 4b and 5b. Similarly, we add the coefficients:

4 (from the first 'b' term) + 5 (from the second 'b' term) equals 9. Thus, when combined, the 'b' terms result in 9b.

Putting these sums together, you find the combined expression is 5a + 9b. This accurately represents the sum of the like terms from the original expression, which is why this option is the correct answer.

This clear methodology of grouping and adding like terms is a fundamental skill in algebra, allowing for straightforward simplification of expressions.