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Simplifying Ab(a + -1b)(a + -2b) = 0 Multiply (a + -1b) * (a + -2b) bA(a(a + -2b) + -1b * (a + -2b)) = 0 bA((a * a + -2b * a) + -1b * (a + -2b)) = 0 Reorder the terms: bA((-2ab + a2) + -1b * (a + -2b)) = 0 bA((-2ab + a2) + -1b * (a + -2b)) = 0 bA(-2ab + a2 + (a * -1b + -2b * -1b)) = 0 bA(-2ab + a2 + (-1ab + 2b2)) = 0 Reorder the terms: bA(-2ab + -1ab + a2 + 2b2) = 0 Combine like terms: -2ab + -1ab = -3ab bA(-3ab + a2 + 2b2) = 0 (-3ab * bA + a2 * bA + 2b2 * bA) = 0 (-3ab2A + a2bA + 2b3A) = 0 Solving -3ab2A + a2bA + 2b3A = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'bA'. bA(-3ab + a2 + 2b2) = 0 Factor a trinomial. bA((a + -2b)(a + -1b)) = 0Subproblem 1
Set the factor 'bA' equal to zero and attempt to solve: Simplifying bA = 0 Solving bA = 0 Move all terms containing a to the left, all other terms to the right. Add '-1bA' to each side of the equation. bA + -1bA = 0 + -1bA Remove the zero: 0 = -1bA Simplifying 0 = -1bA The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(a + -2b)' equal to zero and attempt to solve: Simplifying a + -2b = 0 Solving a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 a + 0 = 0 + 2b a = 0 + 2b Remove the zero: a = 2b Simplifying a = 2bSubproblem 3
Set the factor '(a + -1b)' equal to zero and attempt to solve: Simplifying 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 = {2b, b}
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