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Simplifying (x2 + 2xy + -4y2) * dx + -1(x2 + -8xy + -4y2) * dy = 0 Reorder the terms: (2xy + x2 + -4y2) * dx + -1(x2 + -8xy + -4y2) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + x2 + -4y2) + -1(x2 + -8xy + -4y2) * dy = 0 (2xy * dx + x2 * dx + -4y2 * dx) + -1(x2 + -8xy + -4y2) * dy = 0 Reorder the terms: (-4dxy2 + 2dx2y + dx3) + -1(x2 + -8xy + -4y2) * dy = 0 (-4dxy2 + 2dx2y + dx3) + -1(x2 + -8xy + -4y2) * dy = 0 Reorder the terms: -4dxy2 + 2dx2y + dx3 + -1(-8xy + x2 + -4y2) * dy = 0 Reorder the terms for easier multiplication: -4dxy2 + 2dx2y + dx3 + -1dy(-8xy + x2 + -4y2) = 0 -4dxy2 + 2dx2y + dx3 + (-8xy * -1dy + x2 * -1dy + -4y2 * -1dy) = 0 -4dxy2 + 2dx2y + dx3 + (8dxy2 + -1dx2y + 4dy3) = 0 Reorder the terms: -4dxy2 + 8dxy2 + 2dx2y + -1dx2y + dx3 + 4dy3 = 0 Combine like terms: -4dxy2 + 8dxy2 = 4dxy2 4dxy2 + 2dx2y + -1dx2y + dx3 + 4dy3 = 0 Combine like terms: 2dx2y + -1dx2y = 1dx2y 4dxy2 + 1dx2y + dx3 + 4dy3 = 0 Solving 4dxy2 + 1dx2y + dx3 + 4dy3 = 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), 'd'. d(4xy2 + x2y + x3 + 4y3) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(4xy2 + x2y + x3 + 4y3)' equal to zero and attempt to solve: Simplifying 4xy2 + x2y + x3 + 4y3 = 0 Solving 4xy2 + x2y + x3 + 4y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4xy2' to each side of the equation. 4xy2 + x2y + x3 + -4xy2 + 4y3 = 0 + -4xy2 Reorder the terms: 4xy2 + -4xy2 + x2y + x3 + 4y3 = 0 + -4xy2 Combine like terms: 4xy2 + -4xy2 = 0 0 + x2y + x3 + 4y3 = 0 + -4xy2 x2y + x3 + 4y3 = 0 + -4xy2 Remove the zero: x2y + x3 + 4y3 = -4xy2 Add '-1x2y' to each side of the equation. x2y + x3 + -1x2y + 4y3 = -4xy2 + -1x2y Reorder the terms: x2y + -1x2y + x3 + 4y3 = -4xy2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + x3 + 4y3 = -4xy2 + -1x2y x3 + 4y3 = -4xy2 + -1x2y Add '-1x3' to each side of the equation. x3 + -1x3 + 4y3 = -4xy2 + -1x2y + -1x3 Combine like terms: x3 + -1x3 = 0 0 + 4y3 = -4xy2 + -1x2y + -1x3 4y3 = -4xy2 + -1x2y + -1x3 Add '-4y3' to each side of the equation. 4y3 + -4y3 = -4xy2 + -1x2y + -1x3 + -4y3 Combine like terms: 4y3 + -4y3 = 0 0 = -4xy2 + -1x2y + -1x3 + -4y3 Simplifying 0 = -4xy2 + -1x2y + -1x3 + -4y3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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