Simplify the expression 3(a - 4) + 2a.

Simplify the expression 3(a - 4) + 2a.

• A. 5a - 12
• B. 5a - 4
• C. 3a - 12
• D. 8a - 12

Answer: (A)

This question tests applying the distributive property and then combining like terms. Distribute the 3 across the parentheses: 3(a - 4) becomes 3a - 12. Then add the remaining 2a to that result: 3a - 12 + 2a. Now combine the like terms a: 3a + 2a = 5a, leaving the -12 as a constant. So the expression simplifies to 5a - 12. The -12 comes from multiplying 3 by -4 and stays there, while the a terms combine to give 5a. If the result lacks the -12 or the 2a term, it wouldn’t match the original expression (for example, 5a - 4 would be missing the -12, 3a - 12 would be missing the +2a, and 8a - 12 would miscount the a terms).

This question tests applying the distributive property and then combining like terms. Distribute the 3 across the parentheses: 3(a - 4) becomes 3a - 12. Then add the remaining 2a to that result: 3a - 12 + 2a. Now combine the like terms a: 3a + 2a = 5a, leaving the -12 as a constant. So the expression simplifies to 5a - 12. The -12 comes from multiplying 3 by -4 and stays there, while the a terms combine to give 5a. If the result lacks the -12 or the 2a term, it wouldn’t match the original expression (for example, 5a - 4 would be missing the -12, 3a - 12 would be missing the +2a, and 8a - 12 would miscount the a terms).