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........1.....0.....-3 y^2....0........y^4

...2y.......2y......4.y^2..2 y^3..4 y^4

.......1...2y.........y^2..2.y^3...5y^4

Resultado de la división inexacta

x^4 - 3x^2y^2 + y^4 = (x - 2y) ( x^3 + 2 y x^2 + y^2 x + 2 y^3) +

+ 5 y^4

Cociente

x^3 + 2 y x^2 + y^2 x + 2 y^3

Resto

5 y^4

= (x⁴ - 3x²y² + y⁴)/(x - 2y)

First term: x⁴/x = x³

x³.(x - 2y) = x⁴ - 2x³y

Rest:

= (x⁴ - 3x²y² + y⁴) - (x⁴ - 2x³y)

= x⁴ - 3x²y² + y⁴ - x⁴ + 2x³y

= 2x³y - 3x²y² + y⁴

Second term: 2x³y/x = 2x²y

2x²y.(x - 2y) = 2x³y - 4x²y²

Rest:

= (2x³y - 3x²y² + y⁴) - (2x³y - 4x²y²)

= 2x³y - 3x²y² + y⁴ - 2x³y + 4x²y²

= x²y² + y⁴

Third term: x²y²/x = xy²

xy².(x - 2y) = x²y² - 2xy³

Rest:

= (x²y² + y⁴) - (x²y² - 2xy³)

= x²y² + y⁴ - x²y² + 2xy³

= 2xy³ + y⁴

Fourth term: 2xy³/x = 2y³

2y³.(x - 2y) = 2xy³ - 4y⁴

Rest:

= (2xy³ + y⁴) - (2xy³ - 4y⁴)

= 2xy³ + y⁴ - 2xy³ + 4y⁴

= 5y⁴ ← this is the remainder