# distributive law

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## 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*).

## distributive law

[di′strib·yəd·iv ′lȯ] (mathematics)

A rule which stipulates how two binary operations on a set shall behave with respect to one another; in particular, if +, ° are two such operations then ° distributes over + means

*a*° (*b*+*c*) = (*a*°*b*) + (*a*°*c*) for all*a,b,c*in the set.Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

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