Category: Elementary algebra

Difference of two squares
In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored according to the identity i
Quadratic formula
In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic for
Proofs involving the addition of natural numbers
This article contains mathematical proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity. These proofs are used in the article Addition
Algebraic fraction
In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are and . Algebraic fractions are subject to the same law
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually sma
Clearing denominators
In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – w
Pointwise product
In mathematics, the pointwise product of two functions is another function, obtained by multiplying the images of the two functions at each value in the domain. If f and g are both functions with doma
Change of variables
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed i
Brahmagupta–Fibonacci identity
In algebra, the Brahmagupta–Fibonacci identity expresses the product of two sums of two squares as a sum of two squares in two different ways. Hence the set of all sums of two squares is closed under
Solving quadratic equations with continued fractions
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is where a ≠ 0. The quadratic equation on a number can be solved using the well-known quadratic for
Unary operation
In mathematics, an unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function f : A → A, w
Unitary method
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
FOIL method
In secondary school, FOIL is a mnemonic for the standard method of multiplying two binomials—hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of t
Two-element Boolean algebra
In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain ar
Equating coefficients
In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that
Linear equation
In mathematics, a linear equation is an equation that may be put in the form where are the variables (or unknowns), and are the coefficients, which are often real numbers. The coefficients may be cons
Algebraic operation
In mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, multiplication, division, raising to a whole number power, and takin
Euler's four-square identity
In mathematics, Euler's four-square identity says that the product of two numbers, each of which is a sum of four squares, is itself a sum of four squares.
Quartic equation
In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is where a ≠ 0. The quartic is the highest order polynomial
Additive identity
In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive
Extraneous and missing solutions
In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the proble
Additive inverse
In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation. For a real number, i
Parallel (operator)
The parallel operator (also known as reduced sum, parallel sum or parallel addition) (pronounced "parallel", following the parallel lines notation from geometry) is a mathematical function which is us
Linearity is the property of a mathematical relationship (function) that can be graphically represented as a straight line. Linearity is closely related to proportionality. Examples in physics include
Cube root
In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex
Transitive relation
In mathematics, a relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Each partial order as well as each equivalenc
Expression (mathematics)
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate number
Carlyle circle
In mathematics, a Carlyle circle (named for Thomas Carlyle) is a certain circle in a coordinate plane associated with a quadratic equation. The circle has the property that the solutions of the quadra
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and its cognates in other languages may have subtl
Associative property
In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, asso
In mathematics, an inequation is a statement that an inequality holds between two values. It is usually written in the form of a pair of expressions denoting the values in question, with a relational
Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs
Zero-product property
In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, This property is also known as the rule of zero product, the null factor law, the mult
Partial fraction decomposition
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operati
Identity (mathematics)
In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value fo
Vieta's formulas
In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (more commonly referred to by the Latinised form of his
Constant term
In mathematics, a constant term is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial the 3 is a constant term. A
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general
Algebraic expression
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by
Nth root
In mathematics, an nth root of a number x is a number r which, when raised to the power n, yields x: where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is calle
Quartic function
In algebra, a quartic function is a function of the form where a is nonzero,which is defined by a polynomial of degree four, called a quartic polynomial. A quartic equation, or equation of the fourth
Rationalisation (mathematics)
In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated. If the denominator is a monomial in some radical, say with k < n,
Quadratic equation
In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers
Brahmagupta's identity
In algebra, Brahmagupta's identity says that, for given , the product of two numbers of the form is itself a number of that form. In other words, the set of such numbers is closed under multiplication
In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.
Distributive property
In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality is always true in elementary algebra.For example, in elementary arithme
Light's associativity test
In mathematics, Light's associativity test is a procedure invented by F. W. Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. The na
Cubic equation
In algebra, a cubic equation in one variable is an equation of the form in which a is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of th
Scaling and shifting
No description available.
Cancelling out
(This article is about cancellation of terms in an equation or in elementary algebra. For the extension of 'invertibility' in abstract algebra, see cancellation property.) Cancelling out is a mathemat
Inequality (mathematics)
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by
Parent function
In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions ha
Elementary algebra
Elementary algebra encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variables (quantities without f
Completing the square
In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k. In other words, completing the square places a per
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse o