Which of these represents the correct combination of the terms 10a + 3b - 7a + 2b?

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

Answer: (A)

To correctly combine the terms (10a + 3b - 7a + 2b), we start by grouping like terms. Like terms are those that have the same variable raised to the same power. In this expression, we have two types of like terms: those with the variable (a) and those with the variable (b).

First, we focus on the terms with (a):

• The terms are (10a) and (-7a).

• When we combine these, (10a - 7a) simplifies to (3a).

Next, we look at the terms with (b):

• The terms are (3b) and (2b).

• When we combine these, (3b + 2b) simplifies to (5b).

Putting these results together gives us the final expression: (3a + 5b). This matches the first choice, confirming it as the correct answer.

The initial simplification process involved correctly identifying which terms could be combined due to sharing the same variable, leading to a clear and accurate final result.