Citedistributive 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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