Equivalent Expressions

SAT Math· difficulty 3/5

Which expression is equivalent to 8x318x^3 - 1?

  • A

    (2x1)(4x22x+1)(2x - 1)(4x^2 - 2x + 1)

  • B

    (2x1)(4x2+2x+1)(2x - 1)(4x^2 + 2x + 1)

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  • C

    (2x1)3(2x - 1)^3

  • D

    (2x+1)(4x22x+1)(2x + 1)(4x^2 - 2x + 1)

Explanation

Difference of cubes: a3b3=(ab)(a2+ab+b2)a^3 - b^3 = (a-b)(a^2 + ab + b^2). With a=2xa = 2x, b=1b = 1: (2x1)(4x2+2x+1)(2x-1)(4x^2 + 2x + 1).

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