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Equivalent Expressions Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. Which of the following is equivalent to 16x² − 24x + 9?

    Answer: (4x − 3)²

    This is a perfect square trinomial: (4x)²−2(4x)(3)+3² = (4x−3)².

  2. Which of the following is equivalent to (x + 3)/(x² + x − 6)?

    Answer: 1/(x − 2)

    Factor denominator: x²+x−6 = (x+3)(x−2); cancel (x+3) to get 1/(x−2).

  3. Which expression is equivalent to 3(2x − 1)² − 3?

    Answer: All of the above

    Expand 3(4x²−4x+1)−3 = 12x²−12x+3−3 = 12x²−12x = 12x(x−1) = 6·2x(x−1); all are equivalent.

  4. Which of the following is equivalent to (x^(1/3))^6?

    Answer: x²

    Using the power of a power rule: (x^(1/3))^6 = x^(1/3 · 6) = x² (since 6/3 = 2).

  5. Which of the following is equivalent to (4x + 2)(x − 3)?

    Answer: 4x² − 10x − 6

    FOIL: 4x·x=4x², 4x·(−3)=−12x, 2·x=2x, 2·(−3)=−6; combine: 4x²+(−12x+2x)−6 = 4x²−10x−6.

  6. Which expression is equivalent to (x² + 6x + 9) / (x + 3)?

    Answer: x + 3

    Factor numerator as (x+3)²; cancel one (x+3) to get x+3.

  7. Which of the following is equivalent to (2/x) + (3/x²)?

    Answer: (2x + 3)/x²

    Common denominator is x²: (2/x) = 2x/x²; adding 3/x² gives (2x+3)/x².