One of the defining properties of algebraic structure with two operations such as ring and field:This property shows how the two operations interact.
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For two binary operations, multiplication distributes over addition on the left or right when the respective displayed identity holds. If multiplication is commutative, either law gives the other. Repeated distribution expands expressions in an incline into finite sums of monomials. This property is distinct from associativity of either operation.
The Distributive Property is a fundamental mathematical principle that describes how multiplication interacts with addition (or subtraction).