a^4+b^4+a^2b^2=(a^2+ab+b^2)(a^2-ab+b^2)

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Solution for a^4+b^4+a^2b^2=(a^2+ab+b^2)(a^2-ab+b^2) equation: 


Simplifying
a4 + b4 + a2b2 = (a2 + ab + b2)(a2 + -1ab + b2)

Reorder the terms:
a2b2 + a4 + b4 = (a2 + ab + b2)(a2 + -1ab + b2)

Reorder the terms:
a2b2 + a4 + b4 = (ab + a2 + b2)(a2 + -1ab + b2)

Reorder the terms:
a2b2 + a4 + b4 = (ab + a2 + b2)(-1ab + a2 + b2)

Multiply (ab + a2 + b2) * (-1ab + a2 + b2)
a2b2 + a4 + b4 = (ab(-1ab + a2 + b2) + a2(-1ab + a2 + b2) + b2(-1ab + a2 + b2))
a2b2 + a4 + b4 = ((-1ab * ab + a2 * ab + b2 * ab) + a2(-1ab + a2 + b2) + b2(-1ab + a2 + b2))

Reorder the terms:
a2b2 + a4 + b4 = ((ab3 + -1a2b2 + a3b) + a2(-1ab + a2 + b2) + b2(-1ab + a2 + b2))
a2b2 + a4 + b4 = ((ab3 + -1a2b2 + a3b) + a2(-1ab + a2 + b2) + b2(-1ab + a2 + b2))
a2b2 + a4 + b4 = (ab3 + -1a2b2 + a3b + (-1ab * a2 + a2 * a2 + b2 * a2) + b2(-1ab + a2 + b2))

Reorder the terms:
a2b2 + a4 + b4 = (ab3 + -1a2b2 + a3b + (a2b2 + -1a3b + a4) + b2(-1ab + a2 + b2))
a2b2 + a4 + b4 = (ab3 + -1a2b2 + a3b + (a2b2 + -1a3b + a4) + b2(-1ab + a2 + b2))
a2b2 + a4 + b4 = (ab3 + -1a2b2 + a3b + a2b2 + -1a3b + a4 + (-1ab * b2 + a2 * b2 + b2 * b2))
a2b2 + a4 + b4 = (ab3 + -1a2b2 + a3b + a2b2 + -1a3b + a4 + (-1ab3 + a2b2 + b4))

Reorder the terms:
a2b2 + a4 + b4 = (ab3 + -1ab3 + -1a2b2 + a2b2 + a2b2 + a3b + -1a3b + a4 + b4)

Combine like terms: ab3 + -1ab3 = 0
a2b2 + a4 + b4 = (0 + -1a2b2 + a2b2 + a2b2 + a3b + -1a3b + a4 + b4)
a2b2 + a4 + b4 = (-1a2b2 + a2b2 + a2b2 + a3b + -1a3b + a4 + b4)

Combine like terms: -1a2b2 + a2b2 = 0
a2b2 + a4 + b4 = (0 + a2b2 + a3b + -1a3b + a4 + b4)
a2b2 + a4 + b4 = (a2b2 + a3b + -1a3b + a4 + b4)

Combine like terms: a3b + -1a3b = 0
a2b2 + a4 + b4 = (a2b2 + 0 + a4 + b4)
a2b2 + a4 + b4 = (a2b2 + a4 + b4)

Add '-1a2b2' to each side of the equation.
a2b2 + a4 + -1a2b2 + b4 = a2b2 + a4 + -1a2b2 + b4

Reorder the terms:
a2b2 + -1a2b2 + a4 + b4 = a2b2 + a4 + -1a2b2 + b4

Combine like terms: a2b2 + -1a2b2 = 0
0 + a4 + b4 = a2b2 + a4 + -1a2b2 + b4
a4 + b4 = a2b2 + a4 + -1a2b2 + b4

Reorder the terms:
a4 + b4 = a2b2 + -1a2b2 + a4 + b4

Combine like terms: a2b2 + -1a2b2 = 0
a4 + b4 = 0 + a4 + b4
a4 + b4 = a4 + b4

Add '-1a4' to each side of the equation.
a4 + -1a4 + b4 = a4 + -1a4 + b4

Combine like terms: a4 + -1a4 = 0
0 + b4 = a4 + -1a4 + b4
b4 = a4 + -1a4 + b4

Combine like terms: a4 + -1a4 = 0
b4 = 0 + b4
b4 = b4

Add '-1b4' to each side of the equation.
b4 + -1b4 = b4 + -1b4

Combine like terms: b4 + -1b4 = 0
0 = b4 + -1b4

Combine like terms: b4 + -1b4 = 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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