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Simplifying (y2 + 2xy) * dx + (x2 + 2xy) * dy = 0 Reorder the terms: (2xy + y2) * dx + (x2 + 2xy) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + y2) + (x2 + 2xy) * dy = 0 (2xy * dx + y2 * dx) + (x2 + 2xy) * dy = 0 Reorder the terms: (dxy2 + 2dx2y) + (x2 + 2xy) * dy = 0 (dxy2 + 2dx2y) + (x2 + 2xy) * dy = 0 Reorder the terms: dxy2 + 2dx2y + (2xy + x2) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 2dx2y + dy(2xy + x2) = 0 dxy2 + 2dx2y + (2xy * dy + x2 * dy) = 0 dxy2 + 2dx2y + (2dxy2 + dx2y) = 0 Reorder the terms: dxy2 + 2dxy2 + 2dx2y + dx2y = 0 Combine like terms: dxy2 + 2dxy2 = 3dxy2 3dxy2 + 2dx2y + dx2y = 0 Combine like terms: 2dx2y + dx2y = 3dx2y 3dxy2 + 3dx2y = 0 Solving 3dxy2 + 3dx2y = 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), '3dxy'. 3dxy(y + x) = 0 Ignore the factor 3.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. The solution to this equation could not be determined.
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