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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 x⁻¹ + x⁻²?

    Answer: (x + 1) / x²

    Write x⁻¹ = 1/x and x⁻² = 1/x²; common denominator x² gives (x+1)/x².

  2. Which expression is equivalent to √(50x⁴)?

    Answer: 5x²√2

    √50 = 5√2 and √(x⁴) = x², so √(50x⁴) = 5x²√2.

  3. Which of the following is equivalent to (2a³b²)(3a²b)?

    Answer: 6a⁵b³

    Multiply coefficients 2×3=6, add exponents: a^(3+2)=a⁵ and b^(2+1)=b³, giving 6a⁵b³.

  4. Which of the following is equivalent to (x + 2)³ − 8?

    Answer: x³ + 6x² + 12x

    Expand (x+2)³ = x³+6x²+12x+8; subtract 8 to get x³+6x²+12x, which factors as x(x²+6x+12).

  5. Which expression is equivalent to (9x² − 6x + 1)?

    Answer: (3x − 1)²

    This is a perfect square trinomial: (3x)²−2(3x)(1)+1² = (3x−1)².

  6. Which of the following is equivalent to (x³ + 27) / (x + 3)?

    Answer: x² − 3x + 9

    Sum of cubes: x³+27 = (x+3)(x²−3x+9); divide by (x+3) to get x²−3x+9.

  7. Which of the following is equivalent to 5x² − 5?

    Answer: 5(x − 1)(x + 1)

    Factor out 5: 5(x²−1) = 5(x−1)(x+1) using difference of squares.