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Examples of structures with two operations that are each distributive over the other are Boolean algebras such as the algebra of sets or the switching algebra. Multiplying sums can be put into words as follows: When a sum is multiplied by a sum, multiply each summand of a sum with each summand of the other sum (keeping track of signs) then add ...
Calculators generally perform operations with the same precedence from left to right, [1] but some programming languages and calculators adopt different conventions. For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation.
In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First ("first" terms of each binomial are multiplied together)
Multiplication symbols are usually omitted, and implied, when there is no operator between two variables or terms, or when a coefficient is used. For example, 3 × x 2 is written as 3x 2, and 2 × x × y is written as 2xy. [5] Sometimes, multiplication symbols are replaced with either a dot or center-dot, so that x × y is written as either x ...
An input scheme known as algebraic operating system (AOS) [7] combines both. [7] This is the name Texas Instruments uses for the input scheme used in some of its calculators. [8] Immediate-execution calculators are based on a mixture of infix and postfix notation: binary operations are done as infix, but unary operations are postfix.
Algebraic operations work in the same way as arithmetic operations, [13] such as addition, subtraction, multiplication, division and exponentiation, [14] and are applied to algebraic variables and terms. Multiplication symbols are usually omitted, and implied when there is no space between two variables or terms, or when a coefficient is used.
An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
Multiplication in group theory is typically notated either by a dot or by juxtaposition (the omission of an operation symbol between elements). So multiplying element a by element b could be notated as a b or ab. When referring to a group via the indication of the set and operation, the dot is used.