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Simplifying 2xy(1 + y2) * dx + -1(1 + x2 + x2y2) * dy = 0 Reorder the terms for easier multiplication: 2xy * dx(1 + y2) + -1(1 + x2 + x2y2) * dy = 0 Multiply xy * dx 2dx2y(1 + y2) + -1(1 + x2 + x2y2) * dy = 0 (1 * 2dx2y + y2 * 2dx2y) + -1(1 + x2 + x2y2) * dy = 0 (2dx2y + 2dx2y3) + -1(1 + x2 + x2y2) * dy = 0 Reorder the terms for easier multiplication: 2dx2y + 2dx2y3 + -1dy(1 + x2 + x2y2) = 0 2dx2y + 2dx2y3 + (1 * -1dy + x2 * -1dy + x2y2 * -1dy) = 0 Reorder the terms: 2dx2y + 2dx2y3 + (-1dx2y + -1dx2y3 + -1dy) = 0 2dx2y + 2dx2y3 + (-1dx2y + -1dx2y3 + -1dy) = 0 Reorder the terms: 2dx2y + -1dx2y + 2dx2y3 + -1dx2y3 + -1dy = 0 Combine like terms: 2dx2y + -1dx2y = 1dx2y 1dx2y + 2dx2y3 + -1dx2y3 + -1dy = 0 Combine like terms: 2dx2y3 + -1dx2y3 = 1dx2y3 1dx2y + 1dx2y3 + -1dy = 0 Solving 1dx2y + 1dx2y3 + -1dy = 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(x2 + x2y2 + -1) = 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 '(x2 + x2y2 + -1)' equal to zero and attempt to solve: Simplifying x2 + x2y2 + -1 = 0 Reorder the terms: -1 + x2 + x2y2 = 0 Solving -1 + x2 + x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + x2 + 1 + x2y2 = 0 + 1 Reorder the terms: -1 + 1 + x2 + x2y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x2 + x2y2 = 0 + 1 x2 + x2y2 = 0 + 1 Combine like terms: 0 + 1 = 1 x2 + x2y2 = 1 Add '-1x2' to each side of the equation. x2 + -1x2 + x2y2 = 1 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y2 = 1 + -1x2 x2y2 = 1 + -1x2 Add '-1x2y2' to each side of the equation. x2y2 + -1x2y2 = 1 + -1x2 + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 = 1 + -1x2 + -1x2y2 Simplifying 0 = 1 + -1x2 + -1x2y2 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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