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Simplifying (a + b)(a + 2b) = 0 Multiply (a + b) * (a + 2b) (a(a + 2b) + b(a + 2b)) = 0 ((a * a + 2b * a) + b(a + 2b)) = 0 Reorder the terms: ((2ab + a2) + b(a + 2b)) = 0 ((2ab + a2) + b(a + 2b)) = 0 (2ab + a2 + (a * b + 2b * b)) = 0 (2ab + a2 + (ab + 2b2)) = 0 Reorder the terms: (2ab + ab + a2 + 2b2) = 0 Combine like terms: 2ab + ab = 3ab (3ab + a2 + 2b2) = 0 Solving 3ab + a2 + 2b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + b)(a + 2b) = 0Subproblem 1
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying 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 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 = -2bSolution
a = {-1b, -2b}
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