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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 4x² − 25?

    Answer: (2x + 5)(2x − 5)

    4x² − 25 = (2x)² − 5² is a difference of squares: (2x + 5)(2x − 5).

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

    Answer: 9x²

    (3x + 2)(3x − 2) = 9x² − 4; adding 4: 9x² − 4 + 4 = 9x².

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

    Answer: x + 2

    Factor: x² − x − 6 = (x − 3)(x + 2); cancel (x − 3): result = x + 2.

  4. Which of the following is equivalent to 2(x + 3)² − 18?

    Answer: 2x(x + 6)

    Expand: 2(x² + 6x + 9) − 18 = 2x² + 12x + 18 − 18 = 2x² + 12x = 2x(x + 6).

  5. Which expression is equivalent to (x³ − 8)/(x − 2)?

    Answer: x² + 2x + 4

    x³ − 8 = (x − 2)(x² + 2x + 4) by the difference of cubes formula; cancel (x − 2).

  6. Which of the following is equivalent to (2x)³?

    Answer: 8x³

    (2x)³ = 2³ · x³ = 8x³.

  7. Which expression is equivalent to 6x² + 7x − 3?

    Answer: (3x − 1)(2x + 3)

    (3x − 1)(2x + 3) = 6x² + 9x − 2x − 3 = 6x² + 7x − 3 ✓.