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PSAT Math Multiple-Choice Practice Question 708

Question: 708

If f(a) = a2 - 12, what is f(b - a)?

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).

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