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Algebraic expression. In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations ( addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number ). [1] For example, 3x2 − 2xy + c is an algebraic expression.
As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both terms. Such combination is called combining like terms, and it is an important tool used for solving equations. Simplifying an expression
Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler (usually shorter), for example. Simplification of algebraic expressions, in computer algebra. Simplification of boolean expressions i.e. logic optimization. Simplification by conjunction elimination in inference in logic yields a simpler ...
Closed-form expression. In mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations ( +, −, ×, /, and integer powers) and function composition. Commonly, the allowed functions are n th root, exponential function, logarithm, and trigonometric ...
In calculus and mathematical analysis, algebraic operation is also used for the operations that may be defined by purely algebraic methods. For example, exponentiation with an integer or rational exponent is an algebraic operation, but not the general exponentiation with a real or complex exponent. Also, the derivative is an operation that is ...
Algebraic equation. In mathematics, an algebraic equation or polynomial equation is an equation of the form , where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, is an algebraic equation with integer coefficients and. is a multivariate polynomial equation over the rationals.
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