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Simplifying a4 + -81b4 = 0 Solving a4 + -81b4 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '81b4' to each side of the equation. a4 + -81b4 + 81b4 = 0 + 81b4 Combine like terms: -81b4 + 81b4 = 0 a4 + 0 = 0 + 81b4 a4 = 0 + 81b4 Remove the zero: a4 = 81b4 Simplifying a4 = 81b4 Combine like terms: 81b4 + -81b4 = 0 a4 + -81b4 = 0 Factor a difference between two squares. (a2 + 9b2)(a2 + -9b2) = 0 Factor a difference between two squares. (a2 + 9b2)((a + 3b)(a + -3b)) = 0Subproblem 1
Set the factor '(a2 + 9b2)' equal to zero and attempt to solve: Simplifying a2 + 9b2 = 0 Solving a2 + 9b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-9b2' to each side of the equation. a2 + 9b2 + -9b2 = 0 + -9b2 Combine like terms: 9b2 + -9b2 = 0 a2 + 0 = 0 + -9b2 a2 = 0 + -9b2 Remove the zero: a2 = -9b2 Simplifying a2 = -9b2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(a + 3b)' equal to zero and attempt to solve: Simplifying a + 3b = 0 Solving a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 a + 0 = 0 + -3b a = 0 + -3b Remove the zero: a = -3b Simplifying a = -3bSubproblem 3
Set the factor '(a + -3b)' equal to zero and attempt to solve: Simplifying a + -3b = 0 Solving a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 a + 0 = 0 + 3b a = 0 + 3b Remove the zero: a = 3b Simplifying a = 3bSolution
a = {-3b, 3b}
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