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Simplifying a3 + -1ab2 = 0 Reorder the terms: -1ab2 + a3 = 0 Solving -1ab2 + a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-1b2 + a2) = 0 Factor a difference between two squares. a((b + a)(-1b + a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(b + a)' equal to zero and attempt to solve: Simplifying b + a = 0 Reorder the terms: a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSubproblem 3
Set the factor '(-1b + a)' equal to zero and attempt to solve: Simplifying -1b + a = 0 Reorder the terms: a + -1b = 0 Solving a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. a + -1b + b = 0 + b Combine like terms: -1b + b = 0 a + 0 = 0 + b a = 0 + b Remove the zero: a = b Simplifying a = bSolution
a = {0, -1b, b}
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