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Simplifying (x + -1a)(x2 + ax + a2) = x3 + -1a3 Reorder the terms: (-1a + x)(x2 + ax + a2) = x3 + -1a3 Reorder the terms: (-1a + x)(ax + a2 + x2) = x3 + -1a3 Multiply (-1a + x) * (ax + a2 + x2) (-1a * (ax + a2 + x2) + x(ax + a2 + x2)) = x3 + -1a3 ((ax * -1a + a2 * -1a + x2 * -1a) + x(ax + a2 + x2)) = x3 + -1a3 Reorder the terms: ((-1ax2 + -1a2x + -1a3) + x(ax + a2 + x2)) = x3 + -1a3 ((-1ax2 + -1a2x + -1a3) + x(ax + a2 + x2)) = x3 + -1a3 (-1ax2 + -1a2x + -1a3 + (ax * x + a2 * x + x2 * x)) = x3 + -1a3 (-1ax2 + -1a2x + -1a3 + (ax2 + a2x + x3)) = x3 + -1a3 Reorder the terms: (-1ax2 + ax2 + -1a2x + a2x + -1a3 + x3) = x3 + -1a3 Combine like terms: -1ax2 + ax2 = 0 (0 + -1a2x + a2x + -1a3 + x3) = x3 + -1a3 (-1a2x + a2x + -1a3 + x3) = x3 + -1a3 Combine like terms: -1a2x + a2x = 0 (0 + -1a3 + x3) = x3 + -1a3 (-1a3 + x3) = x3 + -1a3 Reorder the terms: -1a3 + x3 = -1a3 + x3 Add 'a3' to each side of the equation. -1a3 + a3 + x3 = -1a3 + a3 + x3 Combine like terms: -1a3 + a3 = 0 0 + x3 = -1a3 + a3 + x3 x3 = -1a3 + a3 + x3 Combine like terms: -1a3 + a3 = 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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