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A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.
Ada K. Dietz (left) and Ruth E. Foster (right) weaving on Lou Tate Little Looms at the Little Loomhouse, Louisville, KY, circa late 1940s. Ada K. Dietz (October 7, 1888 – January 12, 1981) was an American weaver best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines a novel method for generating weaving patterns based on algebraic patterns.
In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power). [6] These operations may be performed on numbers, in which case they are often called arithmetic operations.
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.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication .
Fundamental theorem of algebra – states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.
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]
Manipulating expressions is the basis of algebra. Factorization is one of the most important methods for expression manipulation for several reasons. If one can put an equation in a factored form E⋅F = 0, then the problem of solving the equation splits into two independent (and generally easier) problems E = 0 and F = 0. When an expression ...