8x^3+y^3-2x-y=(2x+y)(4x^2-2xy+y^2-1)

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Solution for 8x^3+y^3-2x-y=(2x+y)(4x^2-2xy+y^2-1) equation: 


Simplifying
8x3 + y3 + -2x + -1y = (2x + y)(4x2 + -2xy + y2 + -1)

Reorder the terms:
-2x + 8x3 + -1y + y3 = (2x + y)(4x2 + -2xy + y2 + -1)

Reorder the terms:
-2x + 8x3 + -1y + y3 = (2x + y)(-1 + -2xy + 4x2 + y2)

Multiply (2x + y) * (-1 + -2xy + 4x2 + y2)
-2x + 8x3 + -1y + y3 = (2x * (-1 + -2xy + 4x2 + y2) + y(-1 + -2xy + 4x2 + y2))
-2x + 8x3 + -1y + y3 = ((-1 * 2x + -2xy * 2x + 4x2 * 2x + y2 * 2x) + y(-1 + -2xy + 4x2 + y2))

Reorder the terms:
-2x + 8x3 + -1y + y3 = ((-2x + 2xy2 + -4x2y + 8x3) + y(-1 + -2xy + 4x2 + y2))
-2x + 8x3 + -1y + y3 = ((-2x + 2xy2 + -4x2y + 8x3) + y(-1 + -2xy + 4x2 + y2))
-2x + 8x3 + -1y + y3 = (-2x + 2xy2 + -4x2y + 8x3 + (-1 * y + -2xy * y + 4x2 * y + y2 * y))

Reorder the terms:
-2x + 8x3 + -1y + y3 = (-2x + 2xy2 + -4x2y + 8x3 + (-2xy2 + 4x2y + -1y + y3))
-2x + 8x3 + -1y + y3 = (-2x + 2xy2 + -4x2y + 8x3 + (-2xy2 + 4x2y + -1y + y3))

Reorder the terms:
-2x + 8x3 + -1y + y3 = (-2x + 2xy2 + -2xy2 + -4x2y + 4x2y + 8x3 + -1y + y3)

Combine like terms: 2xy2 + -2xy2 = 0
-2x + 8x3 + -1y + y3 = (-2x + 0 + -4x2y + 4x2y + 8x3 + -1y + y3)
-2x + 8x3 + -1y + y3 = (-2x + -4x2y + 4x2y + 8x3 + -1y + y3)

Combine like terms: -4x2y + 4x2y = 0
-2x + 8x3 + -1y + y3 = (-2x + 0 + 8x3 + -1y + y3)
-2x + 8x3 + -1y + y3 = (-2x + 8x3 + -1y + y3)

Add '2x' to each side of the equation.
-2x + 8x3 + -1y + 2x + y3 = -2x + 8x3 + -1y + 2x + y3

Reorder the terms:
-2x + 2x + 8x3 + -1y + y3 = -2x + 8x3 + -1y + 2x + y3

Combine like terms: -2x + 2x = 0
0 + 8x3 + -1y + y3 = -2x + 8x3 + -1y + 2x + y3
8x3 + -1y + y3 = -2x + 8x3 + -1y + 2x + y3

Reorder the terms:
8x3 + -1y + y3 = -2x + 2x + 8x3 + -1y + y3

Combine like terms: -2x + 2x = 0
8x3 + -1y + y3 = 0 + 8x3 + -1y + y3
8x3 + -1y + y3 = 8x3 + -1y + y3

Add '-8x3' to each side of the equation.
8x3 + -1y + -8x3 + y3 = 8x3 + -1y + -8x3 + y3

Reorder the terms:
8x3 + -8x3 + -1y + y3 = 8x3 + -1y + -8x3 + y3

Combine like terms: 8x3 + -8x3 = 0
0 + -1y + y3 = 8x3 + -1y + -8x3 + y3
-1y + y3 = 8x3 + -1y + -8x3 + y3

Reorder the terms:
-1y + y3 = 8x3 + -8x3 + -1y + y3

Combine like terms: 8x3 + -8x3 = 0
-1y + y3 = 0 + -1y + y3
-1y + y3 = -1y + y3

Add 'y' to each side of the equation.
-1y + y + y3 = -1y + y + y3

Combine like terms: -1y + y = 0
0 + y3 = -1y + y + y3
y3 = -1y + y + y3

Combine like terms: -1y + y = 0
y3 = 0 + y3
y3 = y3

Add '-1y3' to each side of the equation.
y3 + -1y3 = y3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = y3 + -1y3

Combine like terms: y3 + -1y3 = 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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