Semplificazione espressioni

[FrancescoLegrottaglie]

Potete semplificarmi questa espressione perfavore?

2(y-3x)^2+2(2x+y)(y-2x)-9x^2-2xy-(2y-x)^2

[Ali Q]

Ecco qui:

2(y-3x)^2+2(2x+y)(y-2x)-9x^2-2xy-(2y-x)^2 =

= 2(y-3x)^2+2(y+2x)(y-2x)-9x^2-2xy-(2y-x)^2 =

= 2(y-3x)^2+2(y^2 -4x^2)-9x^2-2xy-(2y-x)^2 =

= 2(y^2 +9x^2 -6xy)+ 2y^2 -8x^2-9x^2-2xy-(4y^2 +x^2 -4xy) =

= 2(y^2 +9x^2 -6xy)+ 2y^2 -17x^2- 2xy- 4y^2 - x^2 +4xy =

= 2(y^2 +9x^2 -6xy) -18x^2- 2y^2 +2xy =

= 2y^2 +18x^2 -12xy -18x^2- 2y^2 +2xy =

= -12xy +2xy = 10 xy

Ciao!!!