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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 + 3)(x² − x + 4)?

    Answer: 2x³ + x² + 5x + 12

    Distribute: 2x·x²=2x³, 2x·(−x)=−2x², 2x·4=8x, 3·x²=3x², 3·(−x)=−3x, 3·4=12; combine: 2x³+(−2x²+3x²)+(8x−3x)+12 = 2x³+x²+5x+12.

  2. Which expression is equivalent to 8x³ − 64?

    Answer: 8(x − 2)(x² + 2x + 4)

    Factor out 8: 8(x³−8) = 8(x−2)(x²+2x+4) using sum/difference of cubes.

  3. Which of the following is equivalent to (4x² − 1) / (2x − 1)?

    Answer: 2x + 1

    4x²−1 = (2x−1)(2x+1); dividing by (2x−1) gives 2x+1.

  4. Which of the following is equivalent to (3x²)⁰ · (2x)³?

    Answer: 8x³

    Any nonzero quantity to the 0 power equals 1, so 1·(2x)³ = 8x³.

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

    Answer: 1/(x − 1)

    Factor denominator: x²−1 = (x+1)(x−1); cancel (x+1) to get 1/(x−1).

  6. Which of the following is equivalent to (a − b)² + 4ab?

    Answer: (a + b)²

    Expand (a−b)² = a²−2ab+b², then add 4ab: a²+2ab+b² = (a+b)².

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

    Answer: x²

    √x = x^(1/2); multiply x^(1/2) · x^(3/2) = x^(1/2 + 3/2) = x².