N° 6 Prodotti Notevoli

${(x^{2} - 3 xy + y^{2})}^{2} - (x^{2} - y^{2}) \cdot (x^{2} + y^{2}) - 11 x^{2} y^{2} + 6 xy (x^{2} + y^{2}) - 2 y^{4} =$

$= x^{4} - 6 x y^{3} + 11 x^{2} y^{2} - 6 x^{3} y + y^{4} - (x^{4} - y^{4}) - 11 x^{2} y^{2} + 6 x^{3} y + 6 x y^{3} - 2 y^{4} =$

$= x^{4} - 6 x y^{3} + 11 x^{2} y^{2} - 6 x^{3} y + y^{4} - x^{4} + y^{4} - 11 x^{2} y^{2} + 6 x^{3} y + 6 x y^{3} - 2 y^{4} =$

$= (1 - 1) x^{4} + (- 6 + 6) x y^{3} + (11 - 11) x^{2} y^{2} + (- 6 + 6) x^{3} y + (1 + 1 - 2) y^{4} = 0$