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Simplifying (am + an)(am + an) = 0 Multiply (am + an) * (am + an) (am(am + an) + an(am + an)) = 0 ((am * am + an * am) + an(am + an)) = 0 Reorder the terms: ((a2mn + a2m2) + an(am + an)) = 0 ((a2mn + a2m2) + an(am + an)) = 0 (a2mn + a2m2 + (am * an + an * an)) = 0 (a2mn + a2m2 + (a2mn + a2n2)) = 0 Reorder the terms: (a2mn + a2mn + a2m2 + a2n2) = 0 Combine like terms: a2mn + a2mn = 2a2mn (2a2mn + a2m2 + a2n2) = 0 Solving 2a2mn + a2m2 + a2n2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'a2'. a2(2mn + m2 + n2) = 0 Factor a trinomial. a2((m + n)(m + n)) = 0Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(m + n)' equal to zero and attempt to solve: Simplifying m + n = 0 Solving m + n = 0 Move all terms containing a to the left, all other terms to the right. Add '-1m' to each side of the equation. m + -1m + n = 0 + -1m Combine like terms: m + -1m = 0 0 + n = 0 + -1m n = 0 + -1m Remove the zero: n = -1m Add '-1n' to each side of the equation. n + -1n = -1m + -1n Combine like terms: n + -1n = 0 0 = -1m + -1n Simplifying 0 = -1m + -1n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(m + n)' equal to zero and attempt to solve: Simplifying m + n = 0 Solving m + n = 0 Move all terms containing a to the left, all other terms to the right. Add '-1m' to each side of the equation. m + -1m + n = 0 + -1m Combine like terms: m + -1m = 0 0 + n = 0 + -1m n = 0 + -1m Remove the zero: n = -1m Add '-1n' to each side of the equation. n + -1n = -1m + -1n Combine like terms: n + -1n = 0 0 = -1m + -1n Simplifying 0 = -1m + -1n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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