SAT Math Multiple Choice Question 882: Answer and Explanation

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Question: 882

12. What is the factored form of?

  • A.
  • B.
  • C.
  • D.

Correct Answer: A



Difficulty: Medium

Category: Passport to Advanced Math / Exponents

Strategic Advice: Whenever you see long polynomials with coefficients that are perfect squares, look for a factoring shortcut, such as recognizing the square of a sum or difference:. While that may not seem immediately applicable here, notice that x6 = (x3)2 and y6 = (y3)2.

Getting to the Answer: To confirm that you can use a factoring shortcut here, mentally "unsquare" the perfect squares on each end of the polynomial. Letting a = 4x3 and b = y3 (because a2 = 16x6 and b2 = y6), you get 2ab = 2(4x3)(y3) = 8x3y3, which is indeed the middle term of the polynomial, so everything checks out. Thus, the expression equals (a - b)2 or (4x3 - y3)2, choice (A).

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