distributive law

distributive law In mathematics, given any two operations, symbolized by * and [symbol], the first operation, *, is distributive over the second, [symbol], if a *( b [symbol] c )=( a * b )[symbol]( 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 Rule of combination in mathematics, in which an operation applied to a combination of terms is equal to the combination of the operation applied to each individual term. Thus, in arithmetic 3 × (2 + 1) = (3 × 2)+(3 × 1) and, in algebra a(x + y) = ax + ay.