r^4-s^4=

Solution for r^4-s^4= equation:

Simplifying
r4 + -1s4 = 0

Solving
r4 + -1s4 = 0

Solving for variable 'r'.

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

Add 's4' to each side of the equation.
r4 + -1s4 + s4 = 0 + s4

Combine like terms: -1s4 + s4 = 0
r4 + 0 = 0 + s4
r4 = 0 + s4
Remove the zero:
r4 = s4

Simplifying
r4 = s4

Combine like terms: s4 + -1s4 = 0
r4 + -1s4 = 0

Factor a difference between two squares.
(r2 + s2)(r2 + -1s2) = 0

Factor a difference between two squares.
(r2 + s2)((r + s)(r + -1s)) = 0

Subproblem 1
Set the factor '(r2 + s2)' equal to zero and attempt to solve:

Simplifying
r2 + s2 = 0

Solving
r2 + s2 = 0

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

Add '-1s2' to each side of the equation.
r2 + s2 + -1s2 = 0 + -1s2

Combine like terms: s2 + -1s2 = 0
r2 + 0 = 0 + -1s2
r2 = 0 + -1s2
Remove the zero:
r2 = -1s2

Simplifying
r2 = -1s2

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 '(r + s)' equal to zero and attempt to solve:

Simplifying
r + s = 0

Solving
r + s = 0

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

Add '-1s' to each side of the equation.
r + s + -1s = 0 + -1s

Combine like terms: s + -1s = 0
r + 0 = 0 + -1s
r = 0 + -1s
Remove the zero:
r = -1s

Simplifying
r = -1s
Subproblem 3
Set the factor '(r + -1s)' equal to zero and attempt to solve:

Simplifying
r + -1s = 0

Solving
r + -1s = 0

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

Add 's' to each side of the equation.
r + -1s + s = 0 + s

Combine like terms: -1s + s = 0
r + 0 = 0 + s
r = 0 + s
Remove the zero:
r = s

Simplifying
r = s
Solution
r = {-1s, s}