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Simplifying (4mn + 8)(4mn + 8) = 0 Reorder the terms: (8 + 4mn)(4mn + 8) = 0 Reorder the terms: (8 + 4mn)(8 + 4mn) = 0 Multiply (8 + 4mn) * (8 + 4mn) (8(8 + 4mn) + 4mn * (8 + 4mn)) = 0 ((8 * 8 + 4mn * 8) + 4mn * (8 + 4mn)) = 0 ((64 + 32mn) + 4mn * (8 + 4mn)) = 0 (64 + 32mn + (8 * 4mn + 4mn * 4mn)) = 0 (64 + 32mn + (32mn + 16m2n2)) = 0 Combine like terms: 32mn + 32mn = 64mn (64 + 64mn + 16m2n2) = 0 Solving 64 + 64mn + 16m2n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '16'. 16(4 + 4mn + m2n2) = 0 Factor a trinomial. 16((2 + mn)(2 + mn)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + mn)' equal to zero and attempt to solve: Simplifying 2 + mn = 0 Solving 2 + mn = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + mn = 0 + -2 Combine like terms: 2 + -2 = 0 0 + mn = 0 + -2 mn = 0 + -2 Combine like terms: 0 + -2 = -2 mn = -2 Divide each side by 'n'. m = -2n-1 Simplifying m = -2n-1Subproblem 2
Set the factor '(2 + mn)' equal to zero and attempt to solve: Simplifying 2 + mn = 0 Solving 2 + mn = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + mn = 0 + -2 Combine like terms: 2 + -2 = 0 0 + mn = 0 + -2 mn = 0 + -2 Combine like terms: 0 + -2 = -2 mn = -2 Divide each side by 'n'. m = -2n-1 Simplifying m = -2n-1Solution
m = {-2n-1, -2n-1}
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