Equivalent Expressions

SAT Math· difficulty 5/5

Which is equivalent to 27x3+127x^3 + 1?

  • A

    (3x+1)(9x23x+1)(3x + 1)(9x^2 - 3x + 1)

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  • B

    (3x1)(9x2+3x+1)(3x - 1)(9x^2 + 3x + 1)

  • C

    (3x+1)(9x2+3x+1)(3x + 1)(9x^2 + 3x + 1)

  • D

    (3x+1)3(3x + 1)^3

Explanation

Sum of cubes: a3+b3=(a+b)(a2ab+b2)a^3 + b^3 = (a + b)(a^2 - ab + b^2). With a=3x,b=1a = 3x, b = 1: (3x+1)(9x23x+1)(3x + 1)(9x^2 - 3x + 1).

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