(x-8y)(x+8y)=x^2-16xy+64y^2

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Solution for (x-8y)(x+8y)=x^2-16xy+64y^2 equation: 


Simplifying
(x + -8y)(x + 8y) = x2 + -16xy + 64y2

Multiply (x + -8y) * (x + 8y)
(x(x + 8y) + -8y * (x + 8y)) = x2 + -16xy + 64y2
((x * x + 8y * x) + -8y * (x + 8y)) = x2 + -16xy + 64y2

Reorder the terms:
((8xy + x2) + -8y * (x + 8y)) = x2 + -16xy + 64y2
((8xy + x2) + -8y * (x + 8y)) = x2 + -16xy + 64y2
(8xy + x2 + (x * -8y + 8y * -8y)) = x2 + -16xy + 64y2
(8xy + x2 + (-8xy + -64y2)) = x2 + -16xy + 64y2

Reorder the terms:
(8xy + -8xy + x2 + -64y2) = x2 + -16xy + 64y2

Combine like terms: 8xy + -8xy = 0
(0 + x2 + -64y2) = x2 + -16xy + 64y2
(x2 + -64y2) = x2 + -16xy + 64y2

Reorder the terms:
x2 + -64y2 = -16xy + x2 + 64y2

Add '-1x2' to each side of the equation.
x2 + -1x2 + -64y2 = -16xy + x2 + -1x2 + 64y2

Combine like terms: x2 + -1x2 = 0
0 + -64y2 = -16xy + x2 + -1x2 + 64y2
-64y2 = -16xy + x2 + -1x2 + 64y2

Combine like terms: x2 + -1x2 = 0
-64y2 = -16xy + 0 + 64y2
-64y2 = -16xy + 64y2

Solving
-64y2 = -16xy + 64y2

Solving for variable 'y'.

Reorder the terms:
16xy + -64y2 + -64y2 = -16xy + 64y2 + 16xy + -64y2

Combine like terms: -64y2 + -64y2 = -128y2
16xy + -128y2 = -16xy + 64y2 + 16xy + -64y2

Reorder the terms:
16xy + -128y2 = -16xy + 16xy + 64y2 + -64y2

Combine like terms: -16xy + 16xy = 0
16xy + -128y2 = 0 + 64y2 + -64y2
16xy + -128y2 = 64y2 + -64y2

Combine like terms: 64y2 + -64y2 = 0
16xy + -128y2 = 0

Factor out the Greatest Common Factor (GCF), '16y'.
16y(x + -8y) = 0

Ignore the factor 16.

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(x + -8y)' equal to zero and attempt to solve:

Simplifying
x + -8y = 0

Solving
x + -8y = 0

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

Add '-1x' to each side of the equation.
x + -1x + -8y = 0 + -1x

Combine like terms: x + -1x = 0
0 + -8y = 0 + -1x
-8y = 0 + -1x
Remove the zero:
-8y = -1x

Divide each side by '-8'.
y = 0.125x

Simplifying
y = 0.125x
Solution
y = {0, 0.125x}

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