SAT Math Multiple Choice Question 930: Answer and Explanation

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Test Information

Question: 930

14. Which of the following expressions is not a factor of 16x4 – 81y4?

  • A.
  • B.
  • C.
  • D.

Correct Answer: C



Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Strategic Advice: Being able to rewrite an expression as an equivalent expression (for example, by factoring it) will certainly earn you points on Test Day.

Getting to the Answer: Examine each of the terms in the expression: Each term is a perfect square and the terms are joined by a minus sign, so the expression is a difference of two squares. Use the factoring rule a2 - b2 = (a + b)(a - b) to factor the expression:

You can eliminate D because (4x2 + 9y2) is one of the factors given. Next, notice that the second factor is another difference of two squares, so you can factor it further using the same rule:

You can now eliminate A and B, leaving (C) as the expression that is not a factor of 16x4 - 81y4.

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