PSAT Math Multiple-Choice Question 151: Answer and Explanation

Question: 151

(2ab² + 5a² - 7a²b) - (2ab² + 7a²b - 3a²)

Which of the following is equivalent to the expression above?

• A. 4a²b⁴ - 21a²b + 35a²b
• B. 4ab² + 8a² - 14a²b
• C. 2a² + 4ab²
• D. 8a² - 14a²b

Correct Answer: D

Explanation:

D

The question asks for the difference of polynomials, so simplify and combine like terms. Do this in Bite-Sized Pieces. Find like terms, such as 2ab² in the first polynomial and 2ab² in the second polynomial. Subtract to get 2ab² - 2ab² = 0. Therefore, the correct answer must not have an ab² term. Eliminate (B) and (C). Now, look at the a² terms. Subtract -3a² from 5a² to get 5a² - (-3a²) = 8a². Eliminate (A), which does not include this term. Only one choice remains. The correct answer is (D).