x^3-y^3=(x-y)(x^2+xy+x^2)

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Solution for x^3-y^3=(x-y)(x^2+xy+x^2) equation: 


Simplifying
x3 + -1y3 = (x + -1y)(x2 + xy + x2)

Reorder the terms:
x3 + -1y3 = (x + -1y)(xy + x2 + x2)

Combine like terms: x2 + x2 = 2x2
x3 + -1y3 = (x + -1y)(xy + 2x2)

Multiply (x + -1y) * (xy + 2x2)
x3 + -1y3 = (x(xy + 2x2) + -1y * (xy + 2x2))
x3 + -1y3 = ((xy * x + 2x2 * x) + -1y * (xy + 2x2))
x3 + -1y3 = ((x2y + 2x3) + -1y * (xy + 2x2))
x3 + -1y3 = (x2y + 2x3 + (xy * -1y + 2x2 * -1y))
x3 + -1y3 = (x2y + 2x3 + (-1xy2 + -2x2y))

Reorder the terms:
x3 + -1y3 = (-1xy2 + x2y + -2x2y + 2x3)

Combine like terms: x2y + -2x2y = -1x2y
x3 + -1y3 = (-1xy2 + -1x2y + 2x3)

Solving
x3 + -1y3 = -1xy2 + -1x2y + 2x3

Solving for variable 'x'.

Reorder the terms:
xy2 + x2y + x3 + -2x3 + -1y3 = -1xy2 + -1x2y + 2x3 + xy2 + x2y + -2x3

Combine like terms: x3 + -2x3 = -1x3
xy2 + x2y + -1x3 + -1y3 = -1xy2 + -1x2y + 2x3 + xy2 + x2y + -2x3

Reorder the terms:
xy2 + x2y + -1x3 + -1y3 = -1xy2 + xy2 + -1x2y + x2y + 2x3 + -2x3

Combine like terms: -1xy2 + xy2 = 0
xy2 + x2y + -1x3 + -1y3 = 0 + -1x2y + x2y + 2x3 + -2x3
xy2 + x2y + -1x3 + -1y3 = -1x2y + x2y + 2x3 + -2x3

Combine like terms: -1x2y + x2y = 0
xy2 + x2y + -1x3 + -1y3 = 0 + 2x3 + -2x3
xy2 + x2y + -1x3 + -1y3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
xy2 + x2y + -1x3 + -1y3 = 0

The solution to this equation could not be determined.

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