a^3(a-b+1)-b^2(a-b+1)=(a^3-b^2)(a-b+1)

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Solution for a^3(a-b+1)-b^2(a-b+1)=(a^3-b^2)(a-b+1) equation: 


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

Reorder the terms:
a3(1 + a + -1b) + -1b2(a + -1b + 1) = (a3 + -1b2)(a + -1b + 1)
(1 * a3 + a * a3 + -1b * a3) + -1b2(a + -1b + 1) = (a3 + -1b2)(a + -1b + 1)

Reorder the terms:
(1a3 + -1a3b + a4) + -1b2(a + -1b + 1) = (a3 + -1b2)(a + -1b + 1)
(1a3 + -1a3b + a4) + -1b2(a + -1b + 1) = (a3 + -1b2)(a + -1b + 1)

Reorder the terms:
1a3 + -1a3b + a4 + -1b2(1 + a + -1b) = (a3 + -1b2)(a + -1b + 1)
1a3 + -1a3b + a4 + (1 * -1b2 + a * -1b2 + -1b * -1b2) = (a3 + -1b2)(a + -1b + 1)

Reorder the terms:
1a3 + -1a3b + a4 + (-1ab2 + -1b2 + 1b3) = (a3 + -1b2)(a + -1b + 1)
1a3 + -1a3b + a4 + (-1ab2 + -1b2 + 1b3) = (a3 + -1b2)(a + -1b + 1)

Reorder the terms:
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (a3 + -1b2)(a + -1b + 1)

Reorder the terms:
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (a3 + -1b2)(1 + a + -1b)

Multiply (a3 + -1b2) * (1 + a + -1b)
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (a3(1 + a + -1b) + -1b2 * (1 + a + -1b))
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = ((1 * a3 + a * a3 + -1b * a3) + -1b2 * (1 + a + -1b))

Reorder the terms:
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = ((1a3 + -1a3b + a4) + -1b2 * (1 + a + -1b))
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = ((1a3 + -1a3b + a4) + -1b2 * (1 + a + -1b))
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (1a3 + -1a3b + a4 + (1 * -1b2 + a * -1b2 + -1b * -1b2))

Reorder the terms:
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (1a3 + -1a3b + a4 + (-1ab2 + -1b2 + 1b3))
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (1a3 + -1a3b + a4 + (-1ab2 + -1b2 + 1b3))

Reorder the terms:
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3)
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = (-1ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3)

Add 'ab2' to each side of the equation.
-1ab2 + 1a3 + -1a3b + a4 + -1b2 + ab2 + 1b3 = -1ab2 + 1a3 + -1a3b + a4 + -1b2 + ab2 + 1b3

Reorder the terms:
-1ab2 + ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = -1ab2 + 1a3 + -1a3b + a4 + -1b2 + ab2 + 1b3

Combine like terms: -1ab2 + ab2 = 0
0 + 1a3 + -1a3b + a4 + -1b2 + 1b3 = -1ab2 + 1a3 + -1a3b + a4 + -1b2 + ab2 + 1b3
1a3 + -1a3b + a4 + -1b2 + 1b3 = -1ab2 + 1a3 + -1a3b + a4 + -1b2 + ab2 + 1b3

Reorder the terms:
1a3 + -1a3b + a4 + -1b2 + 1b3 = -1ab2 + ab2 + 1a3 + -1a3b + a4 + -1b2 + 1b3

Combine like terms: -1ab2 + ab2 = 0
1a3 + -1a3b + a4 + -1b2 + 1b3 = 0 + 1a3 + -1a3b + a4 + -1b2 + 1b3
1a3 + -1a3b + a4 + -1b2 + 1b3 = 1a3 + -1a3b + a4 + -1b2 + 1b3

Add '-1a3' to each side of the equation.
1a3 + -1a3b + a4 + -1b2 + -1a3 + 1b3 = 1a3 + -1a3b + a4 + -1b2 + -1a3 + 1b3

Reorder the terms:
1a3 + -1a3 + -1a3b + a4 + -1b2 + 1b3 = 1a3 + -1a3b + a4 + -1b2 + -1a3 + 1b3

Combine like terms: 1a3 + -1a3 = 0
0 + -1a3b + a4 + -1b2 + 1b3 = 1a3 + -1a3b + a4 + -1b2 + -1a3 + 1b3
-1a3b + a4 + -1b2 + 1b3 = 1a3 + -1a3b + a4 + -1b2 + -1a3 + 1b3

Reorder the terms:
-1a3b + a4 + -1b2 + 1b3 = 1a3 + -1a3 + -1a3b + a4 + -1b2 + 1b3

Combine like terms: 1a3 + -1a3 = 0
-1a3b + a4 + -1b2 + 1b3 = 0 + -1a3b + a4 + -1b2 + 1b3
-1a3b + a4 + -1b2 + 1b3 = -1a3b + a4 + -1b2 + 1b3

Add 'a3b' to each side of the equation.
-1a3b + a4 + -1b2 + a3b + 1b3 = -1a3b + a4 + -1b2 + a3b + 1b3

Reorder the terms:
-1a3b + a3b + a4 + -1b2 + 1b3 = -1a3b + a4 + -1b2 + a3b + 1b3

Combine like terms: -1a3b + a3b = 0
0 + a4 + -1b2 + 1b3 = -1a3b + a4 + -1b2 + a3b + 1b3
a4 + -1b2 + 1b3 = -1a3b + a4 + -1b2 + a3b + 1b3

Reorder the terms:
a4 + -1b2 + 1b3 = -1a3b + a3b + a4 + -1b2 + 1b3

Combine like terms: -1a3b + a3b = 0
a4 + -1b2 + 1b3 = 0 + a4 + -1b2 + 1b3
a4 + -1b2 + 1b3 = a4 + -1b2 + 1b3

Add '-1a4' to each side of the equation.
a4 + -1b2 + -1a4 + 1b3 = a4 + -1b2 + -1a4 + 1b3

Reorder the terms:
a4 + -1a4 + -1b2 + 1b3 = a4 + -1b2 + -1a4 + 1b3

Combine like terms: a4 + -1a4 = 0
0 + -1b2 + 1b3 = a4 + -1b2 + -1a4 + 1b3
-1b2 + 1b3 = a4 + -1b2 + -1a4 + 1b3

Reorder the terms:
-1b2 + 1b3 = a4 + -1a4 + -1b2 + 1b3

Combine like terms: a4 + -1a4 = 0
-1b2 + 1b3 = 0 + -1b2 + 1b3
-1b2 + 1b3 = -1b2 + 1b3

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

Combine like terms: -1b2 + b2 = 0
0 + 1b3 = -1b2 + b2 + 1b3
1b3 = -1b2 + b2 + 1b3

Combine like terms: -1b2 + b2 = 0
1b3 = 0 + 1b3
1b3 = 1b3

Add '-1b3' to each side of the equation.
1b3 + -1b3 = 1b3 + -1b3

Combine like terms: 1b3 + -1b3 = 0
0 = 1b3 + -1b3

Combine like terms: 1b3 + -1b3 = 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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