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Equivalent Expressions

SAT Math· difficulty 4/5

Which is equivalent to x4−16x^4 - 16?

  • A

    (x2−4)(x2−4)(x^2 - 4)(x^2 - 4)

  • B

    (x−2)4(x - 2)^4

  • C

    (x2−4)2(x^2 - 4)^2

  • D

    (x−2)(x+2)(x2+4)(x - 2)(x + 2)(x^2 + 4)

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Explanation

x4−16=(x2)2−42=(x2−4)(x2+4)=(x−2)(x+2)(x2+4)x^4 - 16 = (x^2)^2 - 4^2 = (x^2 - 4)(x^2 + 4) = (x - 2)(x + 2)(x^2 + 4).

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