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Factor x^3 + 27

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Answer
(x+3)(x2−3x+9)\boxed{(x + 3)(x^2 - 3x + 9)}

Multiplying the factors back together yields the original expression x3+27x^3 + 27.

Problem: Factor the expression x3+27x^3 + 27.

Steps

  1. Rewrite as a sum of cubes
    x3+33x^3 + 3^3
  2. Apply the sum of cubes formula (a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a+b)(a^2 - ab + b^2))
    (x+3)(x2−3x+32)(x + 3)(x^2 - 3x + 3^2)
  3. Simplify the expression
    (x+3)(x2−3x+9)(x + 3)(x^2 - 3x + 9)

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