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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 + 4)(x + 4) − 16?

    Answer: x² + 8x

    Expand (x+4)² = x²+8x+16, then subtract 16 to get x²+8x.

  2. Which expression is equivalent to (15x³ − 10x²) / (5x)?

    Answer: 3x² − 2x

    Divide each term: 15x³/5x = 3x² and −10x²/5x = −2x, giving 3x²−2x.

  3. Which of the following is equivalent to (n − 7)(n + 7) + 49?

    Answer: n²

    Using difference of squares: (n−7)(n+7) = n²−49, then n²−49+49 = n².

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

    Answer: x

    Expand: 6x²−2x − (6x²−3x) = 6x²−2x−6x²+3x = x.

  5. Which of the following is equivalent to (x² + 2x − 15) / (x + 5)?

    Answer: x − 3

    Factor the numerator as (x+5)(x−3), cancel (x+5) to get x−3.

  6. Which expression is equivalent to (4x + 8) / (x² + 4x + 4)?

    Answer: 4 / (x + 2)

    Factor: numerator = 4(x+2), denominator = (x+2)², so the ratio is 4/(x+2).

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

    Answer: −60x

    Using a²−b² = (a−b)(a+b): let a = 3x−5, b = 3x+5; a−b = −10, a+b = 6x−0 = 6x, so product = −60x.