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Simplifying (x^{3}+ y^{5})(x^{3}+ -1y^{5}) = 0 Multiply (x^{3}+ y^{5}) * (x^{3}+ -1y^{5}) (x^{3}(x^{3}+ -1y^{5}) + y^{5}(x^{3}+ -1y^{5})) = 0 ((x^{3}* x^{3}+ -1y^{5}* x^{3}) + y^{5}(x^{3}+ -1y^{5})) = 0 Reorder the terms: ((-1x^{3}y^{5}+ x^{6}) + y^{5}(x^{3}+ -1y^{5})) = 0 ((-1x^{3}y^{5}+ x^{6}) + y^{5}(x^{3}+ -1y^{5})) = 0 (-1x^{3}y^{5}+ x^{6}+ (x^{3}* y^{5}+ -1y^{5}* y^{5})) = 0 (-1x^{3}y^{5}+ x^{6}+ (x^{3}y^{5}+ -1y^{10})) = 0 Reorder the terms: (-1x^{3}y^{5}+ x^{3}y^{5}+ x^{6}+ -1y^{10}) = 0 Combine like terms: -1x^{3}y^{5}+ x^{3}y^{5}= 0 (0 + x^{6}+ -1y^{10}) = 0 (x^{6}+ -1y^{10}) = 0 Solving x^{6}+ -1y^{10}= 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y^{10}' to each side of the equation. x^{6}+ -1y^{10}+ y^{10}= 0 + y^{10}Combine like terms: -1y^{10}+ y^{10}= 0 x^{6}+ 0 = 0 + y^{10}x^{6}= 0 + y^{10}Remove the zero: x^{6}= y^{10}Simplifying x^{6}= y^{10}Combine like terms: y^{10}+ -1y^{10}= 0 x^{6}+ -1y^{10}= 0 Factor a difference between two squares. (x^{3}+ y^{5})(x^{3}+ -1y^{5}) = 0## Subproblem 1

Set the factor '(x^{3}+ y^{5})' equal to zero and attempt to solve: Simplifying x^{3}+ y^{5}= 0 Solving x^{3}+ y^{5}= 0 Move all terms containing x to the left, all other terms to the right. Add '-1y^{5}' to each side of the equation. x^{3}+ y^{5}+ -1y^{5}= 0 + -1y^{5}Combine like terms: y^{5}+ -1y^{5}= 0 x^{3}+ 0 = 0 + -1y^{5}x^{3}= 0 + -1y^{5}Remove the zero: x^{3}= -1y^{5}Simplifying x^{3}= -1y^{5}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^{3}+ -1y^{5})' equal to zero and attempt to solve: Simplifying x^{3}+ -1y^{5}= 0 Solving x^{3}+ -1y^{5}= 0 Move all terms containing x to the left, all other terms to the right. Add 'y^{5}' to each side of the equation. x^{3}+ -1y^{5}+ y^{5}= 0 + y^{5}Combine like terms: -1y^{5}+ y^{5}= 0 x^{3}+ 0 = 0 + y^{5}x^{3}= 0 + y^{5}Remove the zero: x^{3}= y^{5}Simplifying x^{3}= y^{5}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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