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Simplifying (y3 + 2xy) * dx + (x2 + 3xy2) * dx = 0 Reorder the terms: (2xy + y3) * dx + (x2 + 3xy2) * dx = 0 Reorder the terms for easier multiplication: dx(2xy + y3) + (x2 + 3xy2) * dx = 0 (2xy * dx + y3 * dx) + (x2 + 3xy2) * dx = 0 Reorder the terms: (dxy3 + 2dx2y) + (x2 + 3xy2) * dx = 0 (dxy3 + 2dx2y) + (x2 + 3xy2) * dx = 0 Reorder the terms: dxy3 + 2dx2y + (3xy2 + x2) * dx = 0 Reorder the terms for easier multiplication: dxy3 + 2dx2y + dx(3xy2 + x2) = 0 dxy3 + 2dx2y + (3xy2 * dx + x2 * dx) = 0 dxy3 + 2dx2y + (3dx2y2 + dx3) = 0 Solving dxy3 + 2dx2y + 3dx2y2 + dx3 = 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), 'dx'. dx(y3 + 2xy + 3xy2 + x2) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(y3 + 2xy + 3xy2 + x2)' equal to zero and attempt to solve: Simplifying y3 + 2xy + 3xy2 + x2 = 0 Reorder the terms: 2xy + 3xy2 + x2 + y3 = 0 Solving 2xy + 3xy2 + x2 + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy' to each side of the equation. 2xy + 3xy2 + x2 + -2xy + y3 = 0 + -2xy Reorder the terms: 2xy + -2xy + 3xy2 + x2 + y3 = 0 + -2xy Combine like terms: 2xy + -2xy = 0 0 + 3xy2 + x2 + y3 = 0 + -2xy 3xy2 + x2 + y3 = 0 + -2xy Remove the zero: 3xy2 + x2 + y3 = -2xy Add '-3xy2' to each side of the equation. 3xy2 + x2 + -3xy2 + y3 = -2xy + -3xy2 Reorder the terms: 3xy2 + -3xy2 + x2 + y3 = -2xy + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 0 + x2 + y3 = -2xy + -3xy2 x2 + y3 = -2xy + -3xy2 Add '-1x2' to each side of the equation. x2 + -1x2 + y3 = -2xy + -3xy2 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y3 = -2xy + -3xy2 + -1x2 y3 = -2xy + -3xy2 + -1x2 Add '-1y3' to each side of the equation. y3 + -1y3 = -2xy + -3xy2 + -1x2 + -1y3 Combine like terms: y3 + -1y3 = 0 0 = -2xy + -3xy2 + -1x2 + -1y3 Simplifying 0 = -2xy + -3xy2 + -1x2 + -1y3 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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