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Simplifying x4a + -1y4a = 0 Solving ax4 + -1ay4 = 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), 'a'. a(x4 + -1y4) = 0 Factor a difference between two squares. a((x2 + y2)(x2 + -1y2)) = 0 Factor a difference between two squares. a((x2 + y2)((x + y)(x + -1y))) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(x2 + y2)' equal to zero and attempt to solve: Simplifying x2 + y2 = 0 Solving x2 + y2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 0 + -1x2 y2 = 0 + -1x2 Remove the zero: y2 = -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x2 + -1y2 Simplifying 0 = -1x2 + -1y2 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 '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y 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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