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Simplifying (y3 + -3x2y) * dx + -1(x3 + -3xy2) * dy = 0 Reorder the terms: (-3x2y + y3) * dx + -1(x3 + -3xy2) * dy = 0 Reorder the terms for easier multiplication: dx(-3x2y + y3) + -1(x3 + -3xy2) * dy = 0 (-3x2y * dx + y3 * dx) + -1(x3 + -3xy2) * dy = 0 Reorder the terms: (dxy3 + -3dx3y) + -1(x3 + -3xy2) * dy = 0 (dxy3 + -3dx3y) + -1(x3 + -3xy2) * dy = 0 Reorder the terms: dxy3 + -3dx3y + -1(-3xy2 + x3) * dy = 0 Reorder the terms for easier multiplication: dxy3 + -3dx3y + -1dy(-3xy2 + x3) = 0 dxy3 + -3dx3y + (-3xy2 * -1dy + x3 * -1dy) = 0 dxy3 + -3dx3y + (3dxy3 + -1dx3y) = 0 Reorder the terms: dxy3 + 3dxy3 + -3dx3y + -1dx3y = 0 Combine like terms: dxy3 + 3dxy3 = 4dxy3 4dxy3 + -3dx3y + -1dx3y = 0 Combine like terms: -3dx3y + -1dx3y = -4dx3y 4dxy3 + -4dx3y = 0 Solving 4dxy3 + -4dx3y = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4dxy'. 4dxy(y2 + -1x2) = 0 Factor a difference between two squares. 4dxy((y + x)(y + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 0 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 '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing d 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 3
Set the factor '(y + -1x)' equal to zero and attempt to solve: Simplifying y + -1x = 0 Reorder the terms: -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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