What is the result of combining 7a + 2b - 3a - b?

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

Answer: (B)

To simplify the expression 7a + 2b - 3a - b, you start by identifying and combining like terms. Like terms are those that contain the same variable to the same power.

First, look at the terms that involve the variable 'a':

• You have 7a and -3a. When you combine these, you add the coefficients:

7 - 3 = 4.

So, the combined term becomes 4a.

Next, look at the terms that involve the variable 'b':

• Here, you have 2b and -b. Again, you add the coefficients, remembering that -b can be thought of as -1b:

2 - 1 = 1.

This means the combined term for 'b' is simply b.

Putting these together, the simplified expression is 4a + b. This aligns with the correct answer, which shows that understanding how to combine like terms is crucial in simplifying algebraic expressions.