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Simplifying a3 + -1b3 = (a + -1b)(a2 + ab + b2) Reorder the terms: a3 + -1b3 = (a + -1b)(ab + a2 + b2) Multiply (a + -1b) * (ab + a2 + b2) a3 + -1b3 = (a(ab + a2 + b2) + -1b * (ab + a2 + b2)) a3 + -1b3 = ((ab * a + a2 * a + b2 * a) + -1b * (ab + a2 + b2)) Reorder the terms: a3 + -1b3 = ((ab2 + a2b + a3) + -1b * (ab + a2 + b2)) a3 + -1b3 = ((ab2 + a2b + a3) + -1b * (ab + a2 + b2)) a3 + -1b3 = (ab2 + a2b + a3 + (ab * -1b + a2 * -1b + b2 * -1b)) a3 + -1b3 = (ab2 + a2b + a3 + (-1ab2 + -1a2b + -1b3)) Reorder the terms: a3 + -1b3 = (ab2 + -1ab2 + a2b + -1a2b + a3 + -1b3) Combine like terms: ab2 + -1ab2 = 0 a3 + -1b3 = (0 + a2b + -1a2b + a3 + -1b3) a3 + -1b3 = (a2b + -1a2b + a3 + -1b3) Combine like terms: a2b + -1a2b = 0 a3 + -1b3 = (0 + a3 + -1b3) a3 + -1b3 = (a3 + -1b3) Add '-1a3' to each side of the equation. a3 + -1a3 + -1b3 = a3 + -1a3 + -1b3 Combine like terms: a3 + -1a3 = 0 0 + -1b3 = a3 + -1a3 + -1b3 -1b3 = a3 + -1a3 + -1b3 Combine like terms: a3 + -1a3 = 0 -1b3 = 0 + -1b3 -1b3 = -1b3 Add 'b3' to each side of the equation. -1b3 + b3 = -1b3 + b3 Combine like terms: -1b3 + b3 = 0 0 = -1b3 + b3 Combine like terms: -1b3 + b3 = 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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