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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 2x² + 5x − 3?

    Answer: (2x − 1)(x + 3)

    (2x − 1)(x + 3) = 2x² + 6x − x − 3 = 2x² + 5x − 3 ✓.

  2. Which of the following is equivalent to ((x²y)/(z))²?

    Answer: x⁴y²/z²

    Apply the power to each part: (x²)² = x⁴, y² = y², z² = z²; result = x⁴y²/z².

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

    Answer: (3x + 1)/3

    Add numerators over common denominator: (2x − 1 + x + 2)/3 = (3x + 1)/3.

  4. Which of the following is equivalent to (x² − 2x − 8)?

    Answer: (x − 4)(x + 2)

    Find two numbers that multiply to −8 and add to −2: −4 and +2; so (x − 4)(x + 2).

  5. Which of the following is equivalent to a⁰ for any nonzero value of a?

    Answer: 1

    Any nonzero number raised to the power 0 equals 1, by definition of the zero exponent rule.

  6. Which of the following is equivalent to (6x³ − 4x² + 2x)/(2x)?

    Answer: 3x² − 2x + 1

    Divide each term: 6x³/2x − 4x²/2x + 2x/2x = 3x² − 2x + 1.

  7. Which of the following is equivalent to (x − 5)(x + 5) − x(x − 10)?

    Answer: 10x − 25

    (x² − 25) − x(x − 10) = x² − 25 − x² + 10x = 10x − 25.