1.f(x;y;z)=2y2−2yz+2zx−2xy=(y2−2yz+z2)+(y2−2xy+x2)−z2+2xz−x2=(y−z)2+(y−x)2−(z−x)2.Let’s make the transformation of variables: y−z=a;y−x=b;z−x=c.We have f(a;b;c)=a2+b2−c2. It is the orthogonal and normal canonical form.2.For all a,b∈N there exists the unique value sin(ab).The domain of the function y=sin(x) is R , and by the properties of this function y=sin(x) it is unambiguous. So "∗" is a binary operation.
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