The distributive property of multiplication over addition states that for all real numbers a, b, and c:

a(b + c) = (ab) + (ac)

and

(b + c)a = (ba) + (ca).

For example:

• 5(3m - 7n) + 3(4m + n) = 5(3m) - 5(7n) + 3(4m) + 3(n) = 15m - 35n + 12m + 3n = 27m - 32n.

Other versions of the distributive property are:

• multiplication over subtraction
• division over addition
• division over subtraction
• exponentiation over multiplication
• exponentiation over division
• differentiation over addition
• differentiation over subtraction
• integration over addition

See also

• associativity
• commutativity