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Simplifying (2a + -2b)(a + 10b) = 0 Multiply (2a + -2b) * (a + 10b) (2a * (a + 10b) + -2b * (a + 10b)) = 0 ((a * 2a + 10b * 2a) + -2b * (a + 10b)) = 0 Reorder the terms: ((20ab + 2a2) + -2b * (a + 10b)) = 0 ((20ab + 2a2) + -2b * (a + 10b)) = 0 (20ab + 2a2 + (a * -2b + 10b * -2b)) = 0 (20ab + 2a2 + (-2ab + -20b2)) = 0 Reorder the terms: (20ab + -2ab + 2a2 + -20b2) = 0 Combine like terms: 20ab + -2ab = 18ab (18ab + 2a2 + -20b2) = 0 Solving 18ab + 2a2 + -20b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(9ab + a2 + -10b2) = 0 Factor a trinomial. 2((a + -1b)(a + 10b)) = 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 + 10b)' equal to zero and attempt to solve: Simplifying a + 10b = 0 Solving a + 10b = 0 Move all terms containing a to the left, all other terms to the right. Add '-10b' to each side of the equation. a + 10b + -10b = 0 + -10b Combine like terms: 10b + -10b = 0 a + 0 = 0 + -10b a = 0 + -10b Remove the zero: a = -10b Simplifying a = -10bSolution
a = {b, -10b}
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