(x^4+y^4)(x^4-y^4)=

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Solution for (x^4+y^4)(x^4-y^4)= equation:


Simplifying
(x4 + y4)(x4 + -1y4) = 0

Multiply (x4 + y4) * (x4 + -1y4)
(x4(x4 + -1y4) + y4(x4 + -1y4)) = 0
((x4 * x4 + -1y4 * x4) + y4(x4 + -1y4)) = 0

Reorder the terms:
((-1x4y4 + x8) + y4(x4 + -1y4)) = 0
((-1x4y4 + x8) + y4(x4 + -1y4)) = 0
(-1x4y4 + x8 + (x4 * y4 + -1y4 * y4)) = 0
(-1x4y4 + x8 + (x4y4 + -1y8)) = 0

Reorder the terms:
(-1x4y4 + x4y4 + x8 + -1y8) = 0

Combine like terms: -1x4y4 + x4y4 = 0
(0 + x8 + -1y8) = 0
(x8 + -1y8) = 0

Solving
x8 + -1y8 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'y8' to each side of the equation.
x8 + -1y8 + y8 = 0 + y8

Combine like terms: -1y8 + y8 = 0
x8 + 0 = 0 + y8
x8 = 0 + y8
Remove the zero:
x8 = y8

Simplifying
x8 = y8

Combine like terms: y8 + -1y8 = 0
x8 + -1y8 = 0

Factor a difference between two squares.
(x4 + y4)(x4 + -1y4) = 0

Factor a difference between two squares.
(x4 + y4)((x2 + y2)(x2 + -1y2)) = 0

Factor a difference between two squares.
(x4 + y4)((x2 + y2)((x + y)(x + -1y))) = 0

Subproblem 1

Set the factor '(x4 + y4)' equal to zero and attempt to solve: Simplifying x4 + y4 = 0 Solving x4 + y4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y4' to each side of the equation. x4 + y4 + -1y4 = 0 + -1y4 Combine like terms: y4 + -1y4 = 0 x4 + 0 = 0 + -1y4 x4 = 0 + -1y4 Remove the zero: x4 = -1y4 Simplifying x4 = -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 '(x2 + y2)' equal to zero and attempt to solve: Simplifying x2 + y2 = 0 Solving x2 + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. x2 + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 x2 + 0 = 0 + -1y2 x2 = 0 + -1y2 Remove the zero: x2 = -1y2 Simplifying x2 = -1y2 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 '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1y

Subproblem 4

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

Solution

x = {-1y, y}

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