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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.
The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
An algebraic expression is an expression built up from algebraic constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by a rational number). [43] For example, 3x 2 − 2xy + c is an algebraic expression.
An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.
The algebraic equations are the basis of a number of areas of modern mathematics: Algebraic number theory is the study of (univariate) algebraic equations over the rationals (that is, with rational coefficients). Galois theory was introduced by Évariste Galois to specify criteria for deciding if an algebraic equation may be solved in terms of ...
Algebraic notation describes the rules and conventions for writing mathematical expressions, as well as the terminology used for talking about parts of expressions. For example, the expression + has the following components: Algebraic expression notation: 1 – power (exponent) 2 – coefficient 3 – term