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Distributive property

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

<math>a(b+c)=(ab)+(ac)<math>

and

<math>(b+c)a=(ba)+(ca).<math>

For example:

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

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