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Simplifying 0 = (x2 + y4)(x2 + -1y4) Multiply (x2 + y4) * (x2 + -1y4) 0 = (x2(x2 + -1y4) + y4(x2 + -1y4)) 0 = ((x2 * x2 + -1y4 * x2) + y4(x2 + -1y4)) Reorder the terms: 0 = ((-1x2y4 + x4) + y4(x2 + -1y4)) 0 = ((-1x2y4 + x4) + y4(x2 + -1y4)) 0 = (-1x2y4 + x4 + (x2 * y4 + -1y4 * y4)) 0 = (-1x2y4 + x4 + (x2y4 + -1y8)) Reorder the terms: 0 = (-1x2y4 + x2y4 + x4 + -1y8) Combine like terms: -1x2y4 + x2y4 = 0 0 = (0 + x4 + -1y8) 0 = (x4 + -1y8) Solving 0 = x4 + -1y8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x4' to each side of the equation. 0 + -1x4 = x4 + -1x4 + -1y8 Remove the zero: -1x4 = x4 + -1x4 + -1y8 Combine like terms: x4 + -1x4 = 0 -1x4 = 0 + -1y8 -1x4 = -1y8 Divide each side by '-1'. x4 = y8 Simplifying x4 = y8 Combine like terms: y8 + -1y8 = 0 x4 + -1y8 = 0 Factor a difference between two squares. (x2 + y4)(x2 + -1y4) = 0 Factor a difference between two squares. (x2 + y4)((x + y2)(x + -1y2)) = 0Subproblem 1
Set the factor '(x2 + y4)' equal to zero and attempt to solve: Simplifying x2 + y4 = 0 Solving x2 + y4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y4' to each side of the equation. x2 + y4 + -1y4 = 0 + -1y4 Combine like terms: y4 + -1y4 = 0 x2 + 0 = 0 + -1y4 x2 = 0 + -1y4 Remove the zero: x2 = -1y4 Simplifying x2 = -1y4 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 '(x + y2)' equal to zero and attempt to solve: Simplifying x + y2 = 0 Solving x + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. x + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 x + 0 = 0 + -1y2 x = 0 + -1y2 Remove the zero: x = -1y2 Simplifying x = -1y2Subproblem 3
Set the factor '(x + -1y2)' equal to zero and attempt to solve: Simplifying x + -1y2 = 0 Solving x + -1y2 = 0 Move all terms containing x to the left, all other terms to the right. Add 'y2' to each side of the equation. x + -1y2 + y2 = 0 + y2 Combine like terms: -1y2 + y2 = 0 x + 0 = 0 + y2 x = 0 + y2 Remove the zero: x = y2 Simplifying x = y2Solution
x = {-1y2, y2}
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