distributive law

distributive law. In mathematics, given any two operations, symbolized by * and ∘, the first operation, *, is distributive over the second, ∘, if a *( b ∘ c ) = ( a * b )∘( a * c ) for all possible choices of a, b, and c. Multiplication, ×, is distributive over addition, +, since for any numbers a, b, and c, a ×( b + c ) = ( a × b )+( a × c ). For example, for the numbers 2, 3, and 4, 2×(3+4) = 14 and (2×3)+(2×4) = 14, meaning that 2×(3+4) = (2×3)+(2×4). Strictly speaking, this law expresses only left distributivity, i.e., a is distributed from the left side of ( b + c ); the corresponding definition for right distributivity is ( a + b )× c = ( a × c )+( b × c ).

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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