uprość wyrażenie (x+y+z)^2-(x-y+z)^2
w
(x+y+z)^2-(x-y+z)^2=(x+y+z)(x+y+z)-[(x-y+z)(x-y+z)]=
=x^2+xy+xz+xy+y^2+yz+xz+zy+z^2-(x^2-xy+xz-xy+y^2-yz+xz-zy+z^2)=
= x^2+y^2+z^2+2xy+2xz+2zy-x^2+xy-xz+xy-y^2+yz-xz+yz-z^2=
=4xy+4zy=4y(x+z)
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w
(x+y+z)^2-(x-y+z)^2=(x+y+z)(x+y+z)-[(x-y+z)(x-y+z)]=
=x^2+xy+xz+xy+y^2+yz+xz+zy+z^2-(x^2-xy+xz-xy+y^2-yz+xz-zy+z^2)=
= x^2+y^2+z^2+2xy+2xz+2zy-x^2+xy-xz+xy-y^2+yz-xz+yz-z^2=
=4xy+4zy=4y(x+z)