x^5+y^5=(x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)

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Solution for x^5+y^5=(x+y)(x^4-x^3y+x^2y^2-xy^3+y^4) equation: 


Simplifying
x5 + y5 = (x + y)(x4 + -1x3y + x2y2 + -1xy3 + y4)

Reorder the terms:
x5 + y5 = (x + y)(-1xy3 + x2y2 + -1x3y + x4 + y4)

Multiply (x + y) * (-1xy3 + x2y2 + -1x3y + x4 + y4)
x5 + y5 = (x(-1xy3 + x2y2 + -1x3y + x4 + y4) + y(-1xy3 + x2y2 + -1x3y + x4 + y4))
x5 + y5 = ((-1xy3 * x + x2y2 * x + -1x3y * x + x4 * x + y4 * x) + y(-1xy3 + x2y2 + -1x3y + x4 + y4))

Reorder the terms:
x5 + y5 = ((xy4 + -1x2y3 + x3y2 + -1x4y + x5) + y(-1xy3 + x2y2 + -1x3y + x4 + y4))
x5 + y5 = ((xy4 + -1x2y3 + x3y2 + -1x4y + x5) + y(-1xy3 + x2y2 + -1x3y + x4 + y4))
x5 + y5 = (xy4 + -1x2y3 + x3y2 + -1x4y + x5 + (-1xy3 * y + x2y2 * y + -1x3y * y + x4 * y + y4 * y))
x5 + y5 = (xy4 + -1x2y3 + x3y2 + -1x4y + x5 + (-1xy4 + x2y3 + -1x3y2 + x4y + y5))

Reorder the terms:
x5 + y5 = (xy4 + -1xy4 + -1x2y3 + x2y3 + x3y2 + -1x3y2 + -1x4y + x4y + x5 + y5)

Combine like terms: xy4 + -1xy4 = 0
x5 + y5 = (0 + -1x2y3 + x2y3 + x3y2 + -1x3y2 + -1x4y + x4y + x5 + y5)
x5 + y5 = (-1x2y3 + x2y3 + x3y2 + -1x3y2 + -1x4y + x4y + x5 + y5)

Combine like terms: -1x2y3 + x2y3 = 0
x5 + y5 = (0 + x3y2 + -1x3y2 + -1x4y + x4y + x5 + y5)
x5 + y5 = (x3y2 + -1x3y2 + -1x4y + x4y + x5 + y5)

Combine like terms: x3y2 + -1x3y2 = 0
x5 + y5 = (0 + -1x4y + x4y + x5 + y5)
x5 + y5 = (-1x4y + x4y + x5 + y5)

Combine like terms: -1x4y + x4y = 0
x5 + y5 = (0 + x5 + y5)
x5 + y5 = (x5 + y5)

Add '-1x5' to each side of the equation.
x5 + -1x5 + y5 = x5 + -1x5 + y5

Combine like terms: x5 + -1x5 = 0
0 + y5 = x5 + -1x5 + y5
y5 = x5 + -1x5 + y5

Combine like terms: x5 + -1x5 = 0
y5 = 0 + y5
y5 = y5

Add '-1y5' to each side of the equation.
y5 + -1y5 = y5 + -1y5

Combine like terms: y5 + -1y5 = 0
0 = y5 + -1y5

Combine like terms: y5 + -1y5 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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