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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 (x² − 4x − 21)/(x − 7)?

    Answer: x + 3

    Factor: x² − 4x − 21 = (x − 7)(x + 3); cancel (x − 7): result = x + 3.

  2. Which of the following is equivalent to 12x²y³ − 8xy²?

    Answer: 4xy²(3xy − 2)

    GCF = 4xy²; 12x²y³/4xy² = 3xy, 8xy²/4xy² = 2; so 4xy²(3xy − 2).

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

    Answer: 4xy

    (x² + 2xy + y²) − (x² − 2xy + y²) = 4xy.

  4. Which of the following is equivalent to (x² + 4)/(x + 2)?

    Answer: x − 2 + 8/(x + 2)

    Polynomial long division: x² + 4 ÷ (x + 2) = x − 2 remainder 8, giving x − 2 + 8/(x + 2).

  5. Which expression is equivalent to 3x(x − 2) + 4(x − 2)?

    Answer: (3x + 4)(x − 2)

    Factor out (x − 2): 3x(x − 2) + 4(x − 2) = (3x + 4)(x − 2).

  6. Which of the following is equivalent to (2x/(x+1)) − (3/(x+1))?

    Answer: (2x − 3)/(x + 1)

    Same denominator: (2x − 3)/(x + 1).

  7. Which of the following is equivalent to (x^4 − 16)/(x² − 4)?

    Answer: x² + 4

    x⁴ − 16 = (x² + 4)(x² − 4); cancel (x² − 4): result = x² + 4.