Szczegółowe wyjaśnienie:
[tex]a)\ u(x,y,z)=x^2y+x^2z+yz;\ w(x,y,z)=2xyz-yz\\\\u(x,y,z)\cdot w(x,y,z)=(x^2y+x^2z+yz)(2xyz-yz)\\\\=2x^3y^2x-x^2y^2z+2x^3yz^2-x^2yz^2+2xy^2z^2-y^2z^2[/tex]
[tex]b)\ u(x,y,z)=3xyz-4xz^2+y^2z;\ w(x,y,z)=x^2y-xy^2+2z\\\\u(x,y,z)\cdot w(x,y,z)=(3xyz-4xz^2+y^2z)(x^2y-xy^2+2z)\\\\=3x^3y^2z-3x^2y^3z+6xyz^2-4x^3yz^2+4x^2y^2z^2-8xz^3+x^2y^3z-xy^4z+2y^2z^2\\\\=3x^3y^2z-2x^2y^3z+6xyz^2-4x^3yz^2+4x^2y^2z^2-8xz^3-xy^4z+2y^2z^2[/tex]
[tex]c)\ u(x,y,z)=xy^2z^2+2xyz^2-xyz;\ w(x,y,z)=x^2+2y^2+3z^2\\\\u(x,y,z)\cdot w(x,y,z)=(xy^2z^2+2xyz^2-xyz)(x^2+2y^2+3z^2)\\\\=x^3y^2z^2+2xy^4z^2+3xy^2z^4+2x^3yz^2+4xy^3z^2+6xyz^4-x^3yz-2xy^3z-3xyz^3[/tex]
