PSAT Math Multiple-Choice Question 708: Answer and Explanation

Question: 708

If f(a) = a² - 12, what is f(b - a)?

• A. a² + b² - 12
• B. a³ - b - 12
• C. a² - 2ab - b² - 12
• D. a² - 2ab + b² - 12

Correct Answer: D

Explanation:

(D) Just plug in (b - a) wherever there is an a in the expression for f(a):

f(b - a) = (b - a)² - 12

Next, use FOIL for (b - a)²:

(b - a)² = (b - a)(b - a) = b²- ab - ab + a­² = b² - 2ab + a²

Plug this back into f(b - a):

f(b - a) = b² - 2ab + a² -12

This can be arranged as f(b - a) = a² - 2ab + b² -12, choice (D).