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Simplifying (x + -1)(x2 + x + 1) = x3 + -1 Reorder the terms: (-1 + x)(x2 + x + 1) = x3 + -1 Reorder the terms: (-1 + x)(1 + x + x2) = x3 + -1 Multiply (-1 + x) * (1 + x + x2) (-1(1 + x + x2) + x(1 + x + x2)) = x3 + -1 ((1 * -1 + x * -1 + x2 * -1) + x(1 + x + x2)) = x3 + -1 ((-1 + -1x + -1x2) + x(1 + x + x2)) = x3 + -1 (-1 + -1x + -1x2 + (1 * x + x * x + x2 * x)) = x3 + -1 (-1 + -1x + -1x2 + (1x + x2 + x3)) = x3 + -1 Reorder the terms: (-1 + -1x + 1x + -1x2 + x2 + x3) = x3 + -1 Combine like terms: -1x + 1x = 0 (-1 + 0 + -1x2 + x2 + x3) = x3 + -1 (-1 + -1x2 + x2 + x3) = x3 + -1 Combine like terms: -1x2 + x2 = 0 (-1 + 0 + x3) = x3 + -1 (-1 + x3) = x3 + -1 Reorder the terms: -1 + x3 = -1 + x3 Add '1' to each side of the equation. -1 + 1 + x3 = -1 + 1 + x3 Combine like terms: -1 + 1 = 0 0 + x3 = -1 + 1 + x3 x3 = -1 + 1 + x3 Combine like terms: -1 + 1 = 0 x3 = 0 + x3 x3 = x3 Add '-1x3' to each side of the equation. x3 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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