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The left distributive law is $x \cdot (y + z) = xy + xz$, and the right distributive law is $(x + y) \cdot z = xz + yz$. Both laws must hold for all arbitrary elements x, y, and z in the field F.

Conditions: The laws apply to all elements x, y, z in the set F.; Multiplication distributes over addition.

The left distributive law is $x \cdot (y + z) = xy + xz$, and the right distributive law is $(x + y) \cdot z = xz + yz$. Both laws must hold for all arbitrary elements x, y, and z in the field F.

Conditions: The laws apply to all elements x, y, z in the set F.; Multiplication distributes over addition.