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Algebraic expression. In mathematics, an algebraic expression is an expression built up from constants (usually, rational or algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots ( fractional powers). [ 1][ 2] [ 3] [better source needed].
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 ...
The process of simplifying expressions involving the square root of an expression involving the square root of another expression involves finding the two solutions of a quadratic equation. Descartes' theorem states that for every four kissing (mutually tangent) circles, their radii satisfy a particular quadratic equation.
Algebra. Elementary algebra studies which values solve equations formed using arithmetical operations. Abstract algebra studies algebraic structures, like the ring of integers given by the set of integers together with operations of addition ( ) and multiplication ( ). Algebra is the branch of mathematics that studies certain abstract systems ...
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 ...
In mathematics, like terms are summands in a sum that differ only by a numerical factor. [ 1] Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly with different coefficients . More generally, when some variable are ...
n. th root. In mathematics, an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: The integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root.
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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