a)
Wiemy, że:
v(x,y)=[u(x,y)]2−2w(x,y)=
Podstawiamy dane wielomiany:
=(2x2−xy)2−2(6x3y2−3x2y2+y4)=
=(2x2−xy)(2x2−xy)−12x3y2+6x2y2−2y4=
=2x2(2x2−xy)−xy(2x2−xy)−12x3y2+6x2y2−2y4=
=4x4−2x3y−2x3y+x2y2−12x3y2+6x2y2−2y4=
=4x4−12x3y2−4x3y+7x2y2−2y4
b)
Wiemy, że:
v(x,y)=[u(x,y)]2−2w(x,y)=
Podstawiamy dane wielomiany:
=(3x2y+2xy2)2−2(2x4y4+4x4y2+3x3y3−xy4)=
=(3x2y+2xy2)(3x2y+2xy2)−4x4y4−8x4y2−6x3y3+2xy4=
=3x2y(3x2y+2xy2)+2xy2(3x2y+2xy2)−4x4y4−8x4y2−6x3y3+2xy4=
=9x4y2+6x3y3+6x3y3+4x2y4−4x4y4−8x4y2−6x3y3+2xy4=
=−4x4y4+x4y2+6x3y3+4x2y4+2xy4
