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Simplifying (a + -1b)(2a + 4b) = 0 Multiply (a + -1b) * (2a + 4b) (a(2a + 4b) + -1b * (2a + 4b)) = 0 ((2a * a + 4b * a) + -1b * (2a + 4b)) = 0 Reorder the terms: ((4ab + 2a2) + -1b * (2a + 4b)) = 0 ((4ab + 2a2) + -1b * (2a + 4b)) = 0 (4ab + 2a2 + (2a * -1b + 4b * -1b)) = 0 (4ab + 2a2 + (-2ab + -4b2)) = 0 Reorder the terms: (4ab + -2ab + 2a2 + -4b2) = 0 Combine like terms: 4ab + -2ab = 2ab (2ab + 2a2 + -4b2) = 0 Solving 2ab + 2a2 + -4b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(ab + a2 + -2b2) = 0 Factor a trinomial. 2((a + -1b)(a + 2b)) = 0 Ignore the factor 2.Subproblem 1
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 = bSubproblem 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 = {b, -2b}
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