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Equivalent Expressions

SAT Math· difficulty 3/5

Which expression is equivalent to (x+2)(x−2)(x+1)(x + 2)(x - 2)(x + 1)?

  • A

    x3−x2−4x+4x^3 - x^2 - 4x + 4

  • B

    x3+x2−4x−4x^3 + x^2 - 4x - 4

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  • C

    x3+x2+4x+4x^3 + x^2 + 4x + 4

  • D

    x3−x2+4x−4x^3 - x^2 + 4x - 4

Explanation

(x+2)(x−2)=x2−4(x+2)(x-2) = x^2 - 4. Then (x2−4)(x+1)=x3+x2−4x−4(x^2 - 4)(x + 1) = x^3 + x^2 - 4x - 4.

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