Distributive law

When, for meeting S, sum + is defined as a product X,

1. 
2. 

But, it is said that this product satisfies a distributive law (British: Distributive property) for the sum if managed about any former a,b,c. Even if the product is like distribution, it says the same thing to the sum. 2 is called the right distributive law the left distributive law with 1 in particular. Of course there are not 1, 2 distinction when an X satisfies commutative law.

The distributive law consists of the following thing.

• The multiplication of real number satisfies a distributive law for addition.
• The multiplication of the line satisfies a distributive law for addition.
• The friendship of the meeting is like distribution for a common part, and the common part is like distribution for the sum. In addition, the common part is like distribution for a Boolean sum.
• Logical sum (or) of the functional symbol is like distribution for logical product (and), and the logical product is like distribution for logical sum. In addition, the logical product is like distribution for EX-OR (xor).

When I think about the defined set of two binary operations, I often assume a distributive law for the other one. For example, I refer to a ring.

Related story

• Development of the multinomial expression
• Factorization
• Associative law
• Commutative law
• Algebraic structure

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