# Distributivity

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In algebra, distributivity is a property of two binary operations which generalises the relationship between addition and multiplication in elementary algebra known as "multiplying out". For these elementary operations it is also known as the distributive law, expressed as

${\displaystyle a\times (b+c)=(a\times b)+(a\times c)}$

Formally, let ${\displaystyle \otimes }$ and ${\displaystyle \oplus }$ be binary operations on a set X. We say that ${\displaystyle \otimes }$ left distributes over ${\displaystyle \oplus }$, or is left distributive, if

${\displaystyle a\otimes (b\oplus c)=(a\otimes b)\oplus (a\otimes c)\,}$

and ${\displaystyle \otimes }$ right distributes over ${\displaystyle \oplus }$, or is right distributive, if

${\displaystyle (b\oplus c)\otimes a=(b\otimes a)\oplus (c\otimes a).\,}$

The laws are of course equivalent if the operation ${\displaystyle \otimes }$ is commutative.