a^3+b^3=(a+b)(a^2-b+b^2)

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Solution for a^3+b^3=(a+b)(a^2-b+b^2) equation: 


Simplifying
a3 + b3 = (a + b)(a2 + -1b + b2)

Multiply (a + b) * (a2 + -1b + b2)
a3 + b3 = (a(a2 + -1b + b2) + b(a2 + -1b + b2))
a3 + b3 = ((a2 * a + -1b * a + b2 * a) + b(a2 + -1b + b2))

Reorder the terms:
a3 + b3 = ((-1ab + ab2 + a3) + b(a2 + -1b + b2))
a3 + b3 = ((-1ab + ab2 + a3) + b(a2 + -1b + b2))
a3 + b3 = (-1ab + ab2 + a3 + (a2 * b + -1b * b + b2 * b))
a3 + b3 = (-1ab + ab2 + a3 + (a2b + -1b2 + b3))

Reorder the terms:
a3 + b3 = (-1ab + ab2 + a2b + a3 + -1b2 + b3)
a3 + b3 = (-1ab + ab2 + a2b + a3 + -1b2 + b3)

Add '-1a3' to each side of the equation.
a3 + -1a3 + b3 = -1ab + ab2 + a2b + a3 + -1b2 + -1a3 + b3

Combine like terms: a3 + -1a3 = 0
0 + b3 = -1ab + ab2 + a2b + a3 + -1b2 + -1a3 + b3
b3 = -1ab + ab2 + a2b + a3 + -1b2 + -1a3 + b3

Reorder the terms:
b3 = -1ab + ab2 + a2b + a3 + -1a3 + -1b2 + b3

Combine like terms: a3 + -1a3 = 0
b3 = -1ab + ab2 + a2b + 0 + -1b2 + b3
b3 = -1ab + ab2 + a2b + -1b2 + b3

Add '-1b3' to each side of the equation.
b3 + -1b3 = -1ab + ab2 + a2b + -1b2 + b3 + -1b3

Combine like terms: b3 + -1b3 = 0
0 = -1ab + ab2 + a2b + -1b2 + b3 + -1b3

Combine like terms: b3 + -1b3 = 0
0 = -1ab + ab2 + a2b + -1b2 + 0
0 = -1ab + ab2 + a2b + -1b2

Solving
0 = -1ab + ab2 + a2b + -1b2

Solving for variable 'a'.
Remove the zero:
ab + -1ab2 + -1a2b + b2 = -1ab + ab2 + a2b + -1b2 + ab + -1ab2 + -1a2b + b2

Reorder the terms:
ab + -1ab2 + -1a2b + b2 = -1ab + ab + ab2 + -1ab2 + a2b + -1a2b + -1b2 + b2

Combine like terms: -1ab + ab = 0
ab + -1ab2 + -1a2b + b2 = 0 + ab2 + -1ab2 + a2b + -1a2b + -1b2 + b2
ab + -1ab2 + -1a2b + b2 = ab2 + -1ab2 + a2b + -1a2b + -1b2 + b2

Combine like terms: ab2 + -1ab2 = 0
ab + -1ab2 + -1a2b + b2 = 0 + a2b + -1a2b + -1b2 + b2
ab + -1ab2 + -1a2b + b2 = a2b + -1a2b + -1b2 + b2

Combine like terms: a2b + -1a2b = 0
ab + -1ab2 + -1a2b + b2 = 0 + -1b2 + b2
ab + -1ab2 + -1a2b + b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
ab + -1ab2 + -1a2b + b2 = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(a + -1ab + -1a2 + b) = 0


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

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(a + -1ab + -1a2 + b)' equal to zero and attempt to solve:

Simplifying
a + -1ab + -1a2 + b = 0

Solving
a + -1ab + -1a2 + b = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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