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Answer to Question #35464 in Abstract Algebra for jifik

Question #35464
xy-[yz-zx-{yx-(3y-xz)-(xy-zy)}]
Expert's answer
xy-[yz-zx-{yx-(3y-xz)-(xy-zy)}]=xy-[yz-zx-{yx-3y+xz-xy+zy}]=xy-[yz-zx-yx+3y-xz+xy-zy]=xy-yz+zx+yx-3y+xz-xy+zy=-yz+zx+yx-3y+xz+zy

If commutativity holds (i.e. xy=yx) the last expression can be simplified: 2zx+yx-3y (for real numbers it is true).

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