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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 + 2y)²?

    Answer: x² + 4xy + 4y²

    Using (a+b)²=a²+2ab+b²: a=x, b=2y → x²+2(x)(2y)+(2y)² = x²+4xy+4y².

  2. Which expression is equivalent to (x³ − x) / x?

    Answer: x² − 1

    Divide each term by x: x³/x = x², (−x)/x = −1; result is x²−1.

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

    Answer: All of the above

    Factor out 4(x+2): 4(x+2)[−(x+2)+1] = 4(x+2)(−x−1); this equals −4(x+2)(x+1), so all listed are equivalent.

  4. Which of the following is equivalent to (a²b − ab²) / ab?

    Answer: a − b

    Factor numerator: ab(a−b); divide by ab to get a−b.

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

    Answer: 25x² − 16

    Difference of squares: (5x)²−4² = 25x²−16.

  6. Which of the following is equivalent to (8x³ + 1) / (2x + 1)?

    Answer: 4x² − 2x + 1

    Sum of cubes: (2x)³+1³ = (2x+1)(4x²−2x+1); divide by (2x+1) to get 4x²−2x+1.

  7. Which of the following is equivalent to 2x³ − 2x?

    Answer: All of the above

    Factor: 2x(x²−1) = 2x(x−1)(x+1); the first two listed forms represent the same expression.