=8x^2y(x^2-2xy+y^2)

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Solution for =8x^2y(x^2-2xy+y^2) equation: 


Simplifying
0 = 8x2y(x2 + -2xy + y2)

Reorder the terms:
0 = 8x2y(-2xy + x2 + y2)
0 = (-2xy * 8x2y + x2 * 8x2y + y2 * 8x2y)

Reorder the terms:
0 = (8x2y3 + -16x3y2 + 8x4y)
0 = (8x2y3 + -16x3y2 + 8x4y)

Solving
0 = 8x2y3 + -16x3y2 + 8x4y

Solving for variable 'x'.
Remove the zero:
-8x2y3 + 16x3y2 + -8x4y = 8x2y3 + -16x3y2 + 8x4y + -8x2y3 + 16x3y2 + -8x4y

Reorder the terms:
-8x2y3 + 16x3y2 + -8x4y = 8x2y3 + -8x2y3 + -16x3y2 + 16x3y2 + 8x4y + -8x4y

Combine like terms: 8x2y3 + -8x2y3 = 0
-8x2y3 + 16x3y2 + -8x4y = 0 + -16x3y2 + 16x3y2 + 8x4y + -8x4y
-8x2y3 + 16x3y2 + -8x4y = -16x3y2 + 16x3y2 + 8x4y + -8x4y

Combine like terms: -16x3y2 + 16x3y2 = 0
-8x2y3 + 16x3y2 + -8x4y = 0 + 8x4y + -8x4y
-8x2y3 + 16x3y2 + -8x4y = 8x4y + -8x4y

Combine like terms: 8x4y + -8x4y = 0
-8x2y3 + 16x3y2 + -8x4y = 0

Factor out the Greatest Common Factor (GCF), '8x2y'.
8x2y(-1y2 + 2xy + -1x2) = 0

Factor a trinomial.
8x2y((-1y + x)(y + -1x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 0

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 '(-1y + x)' equal to zero and attempt to solve:

Simplifying
-1y + x = 0

Reorder the terms:
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

Subproblem 3
Set the factor '(y + -1x)' equal to zero and attempt to solve:

Simplifying
y + -1x = 0

Reorder the terms:
-1x + y = 0

Solving
-1x + y = 0

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

Add '-1y' to each side of the equation.
-1x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-1x + 0 = 0 + -1y
-1x = 0 + -1y
Remove the zero:
-1x = -1y

Divide each side by '-1'.
x = y

Simplifying
x = y
Solution
x = {y, y}

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