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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 (2x + 1)(x² − 3x + 2)?

    Answer: 2x³ − 5x² + x + 2

    Expand: 2x(x² − 3x + 2) + 1(x² − 3x + 2) = 2x³ − 6x² + 4x + x² − 3x + 2 = 2x³ − 5x² + x + 2.

  2. If 3x² − 27 = 0, which factored form represents the left side?

    Answer: 3(x − 3)(x + 3)

    3x² − 27 = 3(x² − 9) = 3(x − 3)(x + 3) by difference of squares.

  3. Which of the following is equivalent to x⁻³?

    Answer: 1/x³

    A negative exponent means taking the reciprocal: x⁻³ = 1/x³.

  4. Which of the following is equivalent to (3x − 2)/5 + (x + 1)/5?

    Answer: (4x − 1)/5

    Same denominator: (3x − 2 + x + 1)/5 = (4x − 1)/5.

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

    Answer: −16x

    (x − 4)² − (x + 4)² = (x² − 8x + 16) − (x² + 8x + 16) = −16x.

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

    Answer: ∛x²

    x^(2/3) = (x²)^(1/3) = ∛(x²), the cube root of x squared.

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

    Answer: 4(x + 2)(x + 1)

    Let u = x + 2: 4u² − 4u − 8 = 4(u² − u − 2) = 4(u − 2)(u + 1) = 4(x)(x + 3) = 4x(x + 3).