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).

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.

单词	distributive law
释义	distributive law distributive law n (Mathematics) maths logic a theorem asserting that one operator can validly be distributed over another. See distribute⁷ 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)=(ab)+(ac) 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.
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