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Simplifying (8xy + y2) * dx + (4x2 + 2xy + -1y2) * dy = 0 Reorder the terms for easier multiplication: dx(8xy + y2) + (4x2 + 2xy + -1y2) * dy = 0 (8xy * dx + y2 * dx) + (4x2 + 2xy + -1y2) * dy = 0 Reorder the terms: (dxy2 + 8dx2y) + (4x2 + 2xy + -1y2) * dy = 0 (dxy2 + 8dx2y) + (4x2 + 2xy + -1y2) * dy = 0 Reorder the terms: dxy2 + 8dx2y + (2xy + 4x2 + -1y2) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 8dx2y + dy(2xy + 4x2 + -1y2) = 0 dxy2 + 8dx2y + (2xy * dy + 4x2 * dy + -1y2 * dy) = 0 dxy2 + 8dx2y + (2dxy2 + 4dx2y + -1dy3) = 0 Reorder the terms: dxy2 + 2dxy2 + 8dx2y + 4dx2y + -1dy3 = 0 Combine like terms: dxy2 + 2dxy2 = 3dxy2 3dxy2 + 8dx2y + 4dx2y + -1dy3 = 0 Combine like terms: 8dx2y + 4dx2y = 12dx2y 3dxy2 + 12dx2y + -1dy3 = 0 Solving 3dxy2 + 12dx2y + -1dy3 = 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), 'dy'. dy(3xy + 12x2 + -1y2) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(3xy + 12x2 + -1y2)' equal to zero and attempt to solve: Simplifying 3xy + 12x2 + -1y2 = 0 Solving 3xy + 12x2 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3xy' to each side of the equation. 3xy + 12x2 + -3xy + -1y2 = 0 + -3xy Reorder the terms: 3xy + -3xy + 12x2 + -1y2 = 0 + -3xy Combine like terms: 3xy + -3xy = 0 0 + 12x2 + -1y2 = 0 + -3xy 12x2 + -1y2 = 0 + -3xy Remove the zero: 12x2 + -1y2 = -3xy Add '-12x2' to each side of the equation. 12x2 + -12x2 + -1y2 = -3xy + -12x2 Combine like terms: 12x2 + -12x2 = 0 0 + -1y2 = -3xy + -12x2 -1y2 = -3xy + -12x2 Add 'y2' to each side of the equation. -1y2 + y2 = -3xy + -12x2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -3xy + -12x2 + y2 Simplifying 0 = -3xy + -12x2 + y2 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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