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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 (3x + 6)/(x² + 2x)?

    Answer: 3/x

    Factor: numerator = 3(x + 2), denominator = x(x + 2); cancel (x + 2): result = 3/x.

  2. Which of the following is equivalent to (p + q)³?

    Answer: p³ + 3p²q + 3pq² + q³

    Using the binomial expansion: (p + q)³ = p³ + 3p²q + 3pq² + q³.

  3. Which of the following is equivalent to x² + 10x + 25 − y²?

    Answer: (x + y + 5)(x − y + 5)

    Group: (x + 5)² − y² = ((x + 5) + y)((x + 5) − y) = (x + y + 5)(x − y + 5).

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

    Answer: 1

    (x − 3)/(x − 3) = 1, for x ≠ 3.

  5. Which of the following is equivalent to 27x³ − 8?

    Answer: (3x − 2)(9x² + 6x + 4)

    Difference of cubes: (3x)³ − 2³ = (3x − 2)((3x)² + (3x)(2) + 4) = (3x − 2)(9x² + 6x + 4).

  6. Which of the following is equivalent to (x² − 6x + 9)/(x − 3)?

    Answer: x − 3

    x² − 6x + 9 = (x − 3)²; cancel one factor of (x − 3): result = x − 3.

  7. Which of the following expressions is equivalent to (1 − x²)/(x² − 1)?

    Answer: −1

    (1 − x²) = −(x² − 1); so (1 − x²)/(x² − 1) = −(x² − 1)/(x² − 1) = −1, for x ≠ ±1.