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