(x^4-1)(x^4-1)=

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Solution for (x^4-1)(x^4-1)= equation:


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

Reorder the terms:
(-1 + x4)(x4 + -1) = 0

Reorder the terms:
(-1 + x4)(-1 + x4) = 0

Multiply (-1 + x4) * (-1 + x4)
(-1(-1 + x4) + x4(-1 + x4)) = 0
((-1 * -1 + x4 * -1) + x4(-1 + x4)) = 0
((1 + -1x4) + x4(-1 + x4)) = 0
(1 + -1x4 + (-1 * x4 + x4 * x4)) = 0
(1 + -1x4 + (-1x4 + x8)) = 0

Combine like terms: -1x4 + -1x4 = -2x4
(1 + -2x4 + x8) = 0

Solving
1 + -2x4 + x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x4)(1 + -1x4) = 0

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

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

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

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

Subproblem 1

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

Subproblem 3

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

Subproblem 4

Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 5

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

Subproblem 6

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

Solution

x = {-1, 1, -1, 1}

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