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In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality ...
In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. Informally, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers.
Thus any distributive meet-semilattice in which binary joins exist is a distributive lattice. A join-semilattice is distributive if and only if the lattice of its ideals (under inclusion) is distributive. [1] This definition of distributivity allows generalizing some statements about distributive lattices to distributive semilattices.
In mathematics, the associative property [1] is a property of some binary operations that rearranging the parentheses in an expression will not change the result. In propositional logic , associativity is a valid rule of replacement for expressions in logical proofs .
Today the commutative property is a well-known and basic property used in most branches of mathematics. The first recorded use of the term commutative was in a memoir by François Servois in 1814, [1] [10] which used the word commutatives when describing functions that have what is now called the commutative property.
The grid method uses the distributive property twice to expand the product, once for the horizontal factor, and once for the vertical factor. Historically the grid calculation (tweaked slightly) was the basis of a method called lattice multiplication , which was the standard method of multiple-digit multiplication developed in medieval Arabic ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.