(x^2+2xy)(x^2-2xy)=

Solution for (x^2+2xy)(x^2-2xy)= equation:

Simplifying
(x2 + 2xy)(x2 + -2xy) = 0

Reorder the terms:
(2xy + x2)(x2 + -2xy) = 0

Reorder the terms:
(2xy + x2)(-2xy + x2) = 0

Multiply (2xy + x2) * (-2xy + x2)
(2xy * (-2xy + x2) + x2(-2xy + x2)) = 0
((-2xy * 2xy + x2 * 2xy) + x2(-2xy + x2)) = 0
((-4x2y2 + 2x3y) + x2(-2xy + x2)) = 0
(-4x2y2 + 2x3y + (-2xy * x2 + x2 * x2)) = 0
(-4x2y2 + 2x3y + (-2x3y + x4)) = 0

Combine like terms: 2x3y + -2x3y = 0
(-4x2y2 + 0 + x4) = 0
(-4x2y2 + x4) = 0

Solving
-4x2y2 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-4y2 + x2) = 0

Factor a difference between two squares.
x2((2y + x)(-2y + x)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(2y + x)' equal to zero and attempt to solve:

Simplifying
2y + x = 0

Reorder the terms:
x + 2y = 0

Solving
x + 2y = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y
Subproblem 3
Set the factor '(-2y + x)' equal to zero and attempt to solve:

Simplifying
-2y + x = 0

Reorder the terms:
x + -2y = 0

Solving
x + -2y = 0

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

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

Simplifying
x = 2y
Solution
x = {0, -2y, 2y}