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Factor x^3 - 8

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Answer
(x−2)(x2+2x+4)\boxed{(x - 2)(x^2 + 2x + 4)}

Multiplying the factors back together yields x3−8x^3 - 8, confirming the result is correct.

Problem: Factor the expression x3−8x^3 - 8.

Steps

  1. Rewrite as a difference of cubes
    x3−23x^3 - 2^3
  2. Apply the difference of cubes formula (a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2) where a=xa = x and b=2b = 2)
    (x−2)(x2+2x+4)(x - 2)(x^2 + 2x + 4)

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