Simplify: 3a + 4b - 2a + 6b.

• A. a + 10b
• B. 10a + 2b
• C. b - a
• D. 5a + 12b

Answer: (A)

To simplify the expression (3a + 4b - 2a + 6b), you start by combining like terms. Like terms are terms that have the same variable raised to the same power.

First, look at the terms involving (a):

• You have (3a) and (-2a). When you combine these, you perform the operation (3a - 2a), which simplifies to (1a) or simply (a).

Next, consider the terms involving (b):

• You have (4b) and (6b). When you combine these, you apply (4b + 6b), which totals (10b).

Now, put together the simplified terms:

• The combined result for (a) is (a) and for (b) it’s (10b).

Thus, the fully simplified expression is (a + 10b), which corresponds to the first choice. Understanding how to combine like terms accurately is crucial for simplifying algebraic expressions efficiently.