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Simplifying (4xy2 + 2y) * dx + (4x2y + 2x) * dy = 0 Reorder the terms for easier multiplication: dx(4xy2 + 2y) + (4x2y + 2x) * dy = 0 (4xy2 * dx + 2y * dx) + (4x2y + 2x) * dy = 0 Reorder the terms: (2dxy + 4dx2y2) + (4x2y + 2x) * dy = 0 (2dxy + 4dx2y2) + (4x2y + 2x) * dy = 0 Reorder the terms: 2dxy + 4dx2y2 + (2x + 4x2y) * dy = 0 Reorder the terms for easier multiplication: 2dxy + 4dx2y2 + dy(2x + 4x2y) = 0 2dxy + 4dx2y2 + (2x * dy + 4x2y * dy) = 0 2dxy + 4dx2y2 + (2dxy + 4dx2y2) = 0 Reorder the terms: 2dxy + 2dxy + 4dx2y2 + 4dx2y2 = 0 Combine like terms: 2dxy + 2dxy = 4dxy 4dxy + 4dx2y2 + 4dx2y2 = 0 Combine like terms: 4dx2y2 + 4dx2y2 = 8dx2y2 4dxy + 8dx2y2 = 0 Solving 4dxy + 8dx2y2 = 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(1 + 2xy) = 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 '(1 + 2xy)' equal to zero and attempt to solve: Simplifying 1 + 2xy = 0 Solving 1 + 2xy = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2xy = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2xy = 0 + -1 2xy = 0 + -1 Combine like terms: 0 + -1 = -1 2xy = -1 Add '-2xy' to each side of the equation. 2xy + -2xy = -1 + -2xy Combine like terms: 2xy + -2xy = 0 0 = -1 + -2xy Simplifying 0 = -1 + -2xy 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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