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

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


Simplifying
a4 + -1b4 = (a + -1b)(a + b)(a2 + b2)

Multiply (a + -1b) * (a + b)
a4 + -1b4 = (a(a + b) + -1b * (a + b))(a2 + b2)
a4 + -1b4 = ((a * a + b * a) + -1b * (a + b))(a2 + b2)

Reorder the terms:
a4 + -1b4 = ((ab + a2) + -1b * (a + b))(a2 + b2)
a4 + -1b4 = ((ab + a2) + -1b * (a + b))(a2 + b2)
a4 + -1b4 = (ab + a2 + (a * -1b + b * -1b))(a2 + b2)
a4 + -1b4 = (ab + a2 + (-1ab + -1b2))(a2 + b2)

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

Combine like terms: ab + -1ab = 0
a4 + -1b4 = (0 + a2 + -1b2)(a2 + b2)
a4 + -1b4 = (a2 + -1b2)(a2 + b2)

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

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

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

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

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

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

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

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

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

Combine like terms: -1b4 + b4 = 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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