PSAT Math Multiple-Choice Question 93: Answer and Explanation

Question: 93

Which of the following is equivalent to the expression ab² - 3ab + 2b - 6?

• A. (a + 2)(b - 3)
• B. (ab + 2)(b - 3)
• C. b(a + 3)(b - 3)
• D. b(ab - 3a) + 2(b - 6)

Correct Answer: B

Explanation:

B

The question asks for an expression that is equivalent to the one given. There are variables in the question and answer choices, so plug in. Make a = 3 and b = 2. The expression in the question becomes (3)(2)² - 3(3)(2) + 2(2) - 6, which simplifies to (3)(4) - 18 + 4 - 6 and then to 12 - 20, which is -8. This is the target value; circle it. Now plug a = 3 and b = 2 into the answer choices to see which ones matches the target value. Choice (A) becomes (3 + 2)(2 - 3), which is (5)(-1) or -5. This doesn't match the target; eliminate (A). Choice (B) becomes [(3)(2) + 2](2 - 3), which is (8)(-1) or -8. This matches the target; keep (B), but check the remaining answer choices just in case. Choice (C) becomes 2(3 + 3)(2 - 3), which is 2(6)(-1) or -12. Eliminate (C). Choice (D) becomes 2[(3)(2) - 3(3)] + 2(2 - 6), which is 2(6 - 9) + 2(-4). This further simplifies to 2(-3) + 2(-4), which becomes -6 - 8 = -14. Eliminate (D). The correct answer is (B).