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Equivalent Expressions

SAT Math· difficulty 3/5

Which expression is equivalent to (2x−3)(x2+4x−1)(2x - 3)(x^2 + 4x - 1)?

  • A

    2x3−11x2+14x+32x^3 - 11x^2 + 14x + 3

  • B

    2x3+5x2+14x+32x^3 + 5x^2 + 14x + 3

  • C

    2x3−5x2−14x−32x^3 - 5x^2 - 14x - 3

  • D

    2x3+5x2−14x+32x^3 + 5x^2 - 14x + 3

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Explanation

2x(x2+4x−1)−3(x2+4x−1)=2x3+8x2−2x−3x2−12x+3=2x3+5x2−14x+32x(x^2 + 4x - 1) - 3(x^2 + 4x - 1) = 2x^3 + 8x^2 - 2x - 3x^2 - 12x + 3 = 2x^3 + 5x^2 - 14x + 3.

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