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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 9x² − 30x + 25?

    Answer: (3x − 5)²

    9x² − 30x + 25 = (3x)² − 2(3x)(5) + 5² = (3x − 5)².

  2. Which expression is equivalent to (x² − 5x + 4)/(x − 1)?

    Answer: x − 4

    Factor: x² − 5x + 4 = (x − 1)(x − 4); cancel (x − 1): result = x − 4.

  3. Which of the following is equivalent to (x^3)(x^−5)?

    Answer: x^−2

    x³ · x⁻⁵ = x^(3 + (−5)) = x^(−2).

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

    Answer: 3(x + 2)/(x − 2)

    (3x + 6)/(x − 2) = 3(x + 2)/(x − 2); this cannot be simplified further.

  5. 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).

  6. Which of the following is equivalent to (4x² − 9)/(2x + 3)?

    Answer: 2x − 3

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

  7. Which of the following is equivalent to (x + 3)/4 − (x − 1)/4?

    Answer: 1

    (x + 3 − (x − 1))/4 = (x + 3 − x + 1)/4 = 4/4 = 1.