What is a variable in algebra? Last Updated : 30 Aug, 2024 Comments Improve Suggest changes Like Article Like Report Answer: Variables in algebra are the unknown values of the expression. They are represented or assumed by letters. Variables always come attached with a coefficient. There are various equations to solve these expressions and get a solution for these unknown values.Algebraic expressions are built up by the combination of coefficients, integers, variables, constants, and operations. Expressions are the combination of numbers and letters to form an equation or formula. In these expressions, the real number is the fixed known value whereas, the letters represent the unknown values. The combination of coefficient, variable, or constant and operation is known as the term. Types of Algebraic expressionsWith the combination of variables, constants, mathematical operators, etc. an algebraic expression is formed. There are majorly three types of algebraic expressions. They are monomial expressions, binomial expressions, and polynomial expressions. Let's take a look at them in detail,Monomial expressionMonomial expressions are algebraic expressions having only one term. For example: 5x is a monomial expression with a coefficient. 5 and variable x.Binomial expressionBinomial expressions are algebraic expressions having two terms. For example, 5x - 2 is a binomial expression with 5 as a coefficient of x, x as a variable, and -2 constant.Polynomial expressionPolynomial expressions are algebraic expressions having more than two terms. For example, ab + bc + ca is a polynomial expression with three terms.Components of an algebraic expressionAs seen in the examples above, there are different components involved and are part of algebraic expression. The components are coefficients, variables, and constants. Lets take a look at their definitions,Coefficient: The fixed values attached to the variable (an unknown value) are known as a coefficient. For example: In 2x - 4 is an expression having 2 as a coefficient of x.Variable: The unknown values represented by letters in an algebraic expression are known as variables.For example: in expression 5x + 1, x is the variable.Constant: Constants are the fixed real numbers in the expression combined with an operation. Constants are not attached with variables. For example: In expression 4y - 3, -3 is a constant.What is a variable in algebra?Answer:An algebraic expression is built up by terms. In terms, we deal with coefficient, variable, constants, and operations. In the expression, 9y - 19 is the coefficient of variable y.y is the unknown value or variable-1 is the constant And, the expression consists of terms. It means it is a binomial expression.Variables are the unknown values of the expression. They are represented or assumed by letters. Variables always come attached with a coefficient. There are various equations to solve these expressions and get a solution for these unknown values.Sample QuestionsQuestion 1: What is a variable expression?Answer:The expression that consists of variables along with numbers and operations is variable expression. For example: 2x + 3y, 5y + 3, etc.Question2: What are numeric expressions?Answer:The expressions consist of numbers and operations but do not include variables. For example: 2 + 10, etc.Question 3: List the types of polynomials?Answer:Linear polynomialQuadratic polynomialCubic polynomialQuestion 4: What are the variables in equation 2y - 3x?Answer:y and x are the variables in the equation and 2 and 3 are coefficients of these variables respectively.Related Articles:What is a term without a variable? Variables and Constant in Algebraic Expression Comment More infoAdvertise with us Next Article Algebraic Expressions in Math: Definition, Example and Equation R reenadevi98412200 Follow Improve Article Tags : Mathematics School Learning Maths MAQ Similar Reads Algebra in Math - Definition, Branches, Basics and Examples Algebra is the branch of mathematics with the following properties.Deals with symbols (or variables) and rules for manipulating these symbols. Elementary (Taught in Schools) Algebra mainly deals with variables and operations like sum, power, subtraction, etc. For example, x + 10 = 100, x2 - 2x + 1 = 4 min read Basics of AlgebraWhat is a variable in algebra?Answer: Variables in algebra are the unknown values of the expression. They are represented or assumed by letters. Variables always come attached with a coefficient. There are various equations to solve these expressions and get a solution for these unknown values.Algebraic expressions are built up 3 min read Algebraic Expressions in Math: Definition, Example and EquationAlgebraic Expression is a mathematical expression that is made of numbers, and variables connected with any arithmetical operation between them. Algebraic forms are used to define unknown conditions in real life or situations that include unknown variables.An algebraic expression is made up of terms 8 min read Like and Unlike Algebraic Terms: Definition and ExamplesLike terms are terms in algebraic expressions that have the same variables raised to the same powers. Like and Unlike Terms are the types of terms in algebra, and we can differentiate between like and unlike terms by simply checking the variables and their powers. We define algebraic terms as the in 7 min read Mathematical Operations on Algebraic Expressions - Algebraic Expressions and Identities | Class 8 MathsThe basic operations that are being used in mathematics (especially in real number systems) are addition, subtraction, multiplication and so on. These operations can also be done on the algebraic expressions. Let us see them in detail. Algebraic expressions (also known as algebraic equations) are de 5 min read Algebraic ExpressionAlgebra Practice Questions Easy LevelAlgebra questions basically involve modeling word problems into equations and then solving them. Some of the very basic formulae that come in handy while solving algebra questions are : (a + b) 2 = a 2 + b 2 + 2 a b(a - b) 2 = a 2 + b 2 - 2 a b(a + b) 2 - (a - b) 2 = 4 a b(a + b) 2 + (a - b) 2 = 2 ( 3 min read Algebraic IdentitiesAlgebraic Identities are fundamental equations in algebra where the left-hand side of the equation is always equal to the right-hand side, regardless of the values of the variables involved. These identities play a crucial role in simplifying algebraic computations and are essential for solving vari 14 min read Factorization of PolynomialFactorization in mathematics refers to the process of expressing a number or an algebraic expression as a product of simpler factors. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, and we can express 12 as 12 = 1 × 12, 2 × 6, or 4 × 3.Similarly, factorization of polynomials involves expre 10 min read Division of Algebraic ExpressionsDivision of algebraic expressions is a key operation in algebra. It is essential for simplifying expressions and solving equations. It is used to perform polynomial long division or synthetic division. Division of algebraic expressions is performed as as division on two whole numbers or fractions. I 6 min read PolynomialsPolynomials| Degree | Types | Properties and ExamplesPolynomials are mathematical expressions made up of variables (often represented by letters like x, y, etc.), constants (like numbers), and exponents (which are non-negative integers). These expressions are combined using addition, subtraction, and multiplication operations.A polynomial can have one 9 min read Types of Polynomials (Based on Terms and Degrees)Types of Polynomials: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. There are mainly four types of polynomials based on degree-constant polynomial (zero degree), linear polynomial ( 1st degree), quadratic polynomial (2n 9 min read Zeros of PolynomialZeros of a Polynomial are those real, imaginary, or complex values when put in the polynomial instead of a variable, the result becomes zero (as the name suggests zero as well). Polynomials are used to model some physical phenomena happening in real life, they are very useful in describing situation 13 min read Geometrical meaning of the Zeroes of a PolynomialAn algebraic identity is an equality that holds for any value of its variables. They are generally used in the factorization of polynomials or simplification of algebraic calculations. A polynomial is just a bunch of algebraic terms added together, for example, p(x) = 4x + 1 is a degree-1 polynomial 8 min read Multiplying Polynomials WorksheetA polynomial is an algebraic expression consisting of variables and coefficients. We can perform various operations on polynomials, including addition, subtraction, multiplication, and division. This worksheet focuses on multiplying polynomials using different methods.Read More: Multiplying Polynomi 4 min read Dividing Polynomials | Long Division | Synthetic Division | Factorization MethodsDividing Polynomials in maths is an arithmetic operation in which one polynomial is divided by another polynomial, where the divisor polynomial must have a degree less than or equal to the Dividend Polynomial otherwise division of polynomial can't take place. The most general form of a polynomial is 13 min read Division Algorithm for PolynomialsPolynomials are those algebraic expressions that contain variables, coefficients, and constants. For Instance, in the polynomial 8x2 + 3z - 7, in this polynomial, 8,3 are the coefficients, x and z are the variables, and 7 is the constant. Just as simple Mathematical operations are applied on numbers 5 min read Division Algorithm Problems and SolutionsPolynomials are made up of algebraic expressions with different degrees. Degree-one polynomials are called linear polynomials, degree-two are called quadratic and degree-three are called cubic polynomials. Zeros of these polynomials are the points where these polynomials become zero. Sometimes it ha 6 min read Remainder TheoremThe Remainder Theorem is a simple yet powerful tool in algebra that helps you quickly find the remainder when dividing a polynomial by a linear polynomial, such as (x - a). Instead of performing long or synthetic division, you can use this theorem to substitute the polynomial and get the remainder d 8 min read Factor TheoremFactor theorem is used for finding the roots of the given polynomial. This theorem is very helpful in finding the factors of the polynomial equation without actually solving them.According to the factor theorem, for any polynomial f(x) of degree n ≥ 1 a linear polynomial (x - a) is the factor of the 10 min read Algebraic Identities of PolynomialsAlgebraic identities are equations that hold true for all values of the variables involved. In the context of polynomials, these identities are particularly useful for simplifying expressions and solving equations.Algebraic Identities of PolynomialsWhat are Algebraic Identities?Algebraic Identities 9 min read Factoring PolynomialsFactoring Polynomials: A basic algebraic concept called factoring polynomials involves breaking down a polynomial equation into simpler parts. Factoring can be used to solve equations, simplify complicated expressions, and locate the roots or zeros of polynomial functions. In several fields of math 9 min read Relationship between Zeroes and Coefficients of a PolynomialPolynomials are algebraic expressions with constants and variables that can be linear i.e. the highest power o the variable is one, quadratic and others. The zeros of the polynomials are the values of the variable (say x) that on substituting in the polynomial give the answer as zero. While the coef 9 min read Linear EquationsLinear Equations in One VariableLinear equation in one variable is the equation that is used for representing the conditions that are dependent on one variable. It is a linear equation i.e. the equation in which the degree of the equation is one, and it only has one variable.A linear equation in one variable is a mathematical stat 7 min read Solving Linear Equations with Variable on both SidesEquations consist of two main components: variables and numbers. Understanding the relationship between these components and how to manipulate them is essential for solving equations.Variable: A variable is a symbol (often a letter like x, y, or z) that represents an unknown or changing quantity.Num 6 min read Graphical Methods of Solving Pair of Linear Equations in Two VariablesA system of linear equations is just a pair of two lines that may or may not intersect. The graph of a linear equation is a line. There are various methods that can be used to solve two linear equations, for example, Substitution Method, Elimination Method, etc. An easy-to-understand and beginner-fr 8 min read Reducing Equations to Simpler Form | Class 8 MathsReducing equations is a method used to simplify complex equations into a more manageable form. This technique is particularly useful when dealing with non-linear equations, which cannot always be solved directly. By applying specific mathematical operations, such as cross-multiplication, these equat 6 min read Linear Equation in Two VariablesLinear Equation in Two Variables: A Linear equation is defined as an equation with the maximum degree of one only, for example, ax = b can be referred to as a linear equation, and when a Linear equation in two variables comes into the picture, it means that the entire equation has 2 variables presen 9 min read Graph of Linear Equations in Two VariablesLinear equations are the first-order equations, i.e. the equations of degree 1. The equations which are used to define any straight line are linear, they are represented as, x + k = 0; These equations have a unique solution and can be represented on number lines very easily. Let's look at linear e 5 min read Equations of Lines Parallel to the x-axis and y-axisLinear Equations allow us to explain a lot of physical phenomena happening around us. For example, A train running between two stations at a constant speed, the speed of a falling object. Even the straight lines we draw on paper can be represented in form of linear equations mathematically. A linear 6 min read Pair of Linear Equations in Two VariablesLinear Equation in two variables are equations with only two variables and the exponent of the variable is 1. This system of equations can have a unique solution, no solution, or an infinite solution according to the given initial condition. Linear equations are used to describe a relationship betwe 11 min read Number of Solutions to a System of Equations AlgebraicallyA statement that two mathematical expressions of one or more variables are identical is called an equation. Linear equations are those in which the powers of all the variables concerned are equal. A linear equation's degree is always one. A solution of the simultaneous pair of linear equations is a 7 min read Solve the Linear Equation using Substitution MethodA linear equation is an equation where the highest power of the variable is always 1. Its graph is always a straight line. A linear equation in one variable has only one unknown with a degree of 1, such as:3x + 4 = 02y = 8m + n = 54a – 3b + c = 7x/2 = 8There are mainly two methods for solving simult 10 min read Cross Multiplication MethodCross multiplication method is one of the basic methods in mathematics that is used to solve the linear equations in two variables. It is one of the easiest to solve a pair of linear equations in two variables. Suppose we have a pair of linear equations in two variables, i.e. a1x + b1y = -c1 and a2 9 min read Equations Reducible to Linear FormEquations Reducible to Linear Form" refers to equations that can be transformed or rewritten into a linear equation. These equations typically involve variables raised to powers other than 1, such as squared terms, cubed terms, or higher. By applying suitable substitutions or transformations, these 9 min read Quadratic EquationsQuadratic EquationsA Quadratic equation is a second-degree polynomial equation that can be represented as ax2 + bx + c = 0. In this equation, x is an unknown variable, a, b, and c are constants, and a is not equal to 0. The solutions of a quadratic equation are known as its roots. These roots can be found using method 12 min read Solving Quadratic EquationsA quadratic equation, typically in the form ax² + bx + c = 0, can be solved using different methods including factoring, completing the square, quadratic formula, and the graph method. While Solving Quadratic Equations we try to find a solution that represent the points where this the condition Q(x) 8 min read Roots of Quadratic EquationThe roots of a quadratic equation are the values of x that satisfy the equation. The roots of a quadratic equation are also called zeros of a quadratic equation. A quadratic equation is generally in the form: ax2 + bx + c = 0Where:a, b, and c are constants (with a ≠0).x represents the variable.Root 13 min read Cubic EquationsCubic Equation FormulaA cubic equation is a polynomial equation of degree three, and it can be written in the general form: ax3 + bx2 + cx + d = 0. Solutions to a cubic equation can be found using various methods, including factoring, synthetic division, or using the cubic formula.In this article, we will learn about cub 6 min read Solving Cubic EquationsCubic Equation is a mathematical equation in which a polynomial of degree 3 is equated to a constant or another polynomial of maximum degree 2. The standard representation of the cubic equation is ax3+bx2+cx+d = 0 where a, b, c, and d are real numbers. Some examples of cubic equation are x3 - 4x2 + 12 min read Sequence and SeriesArithmetic Progression in MathsArithmetic Progression (AP) or Arithmetic Sequence is simply a sequence of numbers such that the difference between any two consecutive terms is constant.Some Real World Examples of APNatural Numbers: 1, 2, 3, 4, 5, . . . with a common difference 1Even Numbers: 2, 4, 6, 8, 10, . . . with a common di 3 min read Arithmetic SeriesAn arithmetic series is the sum of the terms of an arithmetic sequence, where an arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. Or we can say that an arithmetic progression can be defined as a sequence of numbers in which for every pair of 5 min read Arithmetic SequenceAn arithmetic sequence or progression is defined as a sequence of numbers in which the difference between one term and the next term remains constant.For example: the given below sequence has a common difference of 1.1 2 3 4 5 . . . n ⇑ ⇑ ⇑ ⇑ ⇑ . . . 1st 2nd 3rd 4th 5th . . . nth TermsThe Arithmetic 8 min read Program to Check Geometric ProgressionA sequence of numbers is called a Geometric progression if the ratio of any two consecutive terms is always the same.In simple terms, A geometric series is a list of numbers where each number, or term, is found by multiplying the previous term by a common ratio r. The general form of Geometric Progr 6 min read Geometric SeriesIn a Geometric Series, every next term is the multiplication of its Previous term by a certain constant, and depending upon the value of the constant, the Series may increase or decrease.Geometric Sequence is given as: a, ar, ar2, ar3, ar4,..... {Infinite Sequence}a, ar, ar2, ar3, ar4, ....... arn { 3 min read Set TheoryRepresentation of a SetSets are defined as collections of well-defined data. In Math, a Set is a tool that helps to classify and collect data belonging to the same category. Even though the elements used in sets are all different from each other, they are all similar as they belong to one group. For instance, a set of dif 8 min read Types Of SetsIn mathematics, a set is defined as a well-defined collection of distinct elements that share a common property. These elements— like numbers, letters, or even other sets are listed in curly brackets "{ }" and represented by capital letters. For example, a set can include days of the week. The diffe 13 min read Universal SetsUniversal Set is a set that has all the elements associated with a given set, without any repetition. Suppose we have two sets P = {1, 3, 5} and Q = {2, 4, 6} then the universal set of P and Q is U = {1, 2, 3, 4, 5, 6}. We generally use U to denote universal sets. Universal Set is a type of set that 6 min read Venn DiagramVenn diagrams are visual tools used to show relationships between different sets. They use overlapping circles to represent how sets intersect, share elements, or stay separate. These diagrams help categorize items, making it easier to understand similarities and differences. In mathematics, Venn di 14 min read Operations on SetsSets are fundamental in mathematics and are collections of distinct objects, considered as a whole. In this article, we will explore the basic operations you can perform on sets, such as union, intersection, difference, and complement. These operations help us understand how sets interact with each 15+ min read Union of SetsUnion of two sets means finding a set containing all the values in both sets. It is denoted using the symbol '∪' and is read as the union. Example 1:If A = {1, 3. 5. 7} and B = {1, 2, 3} then A∪B is read as A union B and its value is,A∪B = {1, 2, 3, 5, 7}Example 2:If A = {1, 3. 5.7} and B = {2, 4} t 12 min read Cartesian Product of SetsThe term 'product' mathematically refers to the result obtained when two or more values are multiplied together. For example, 45 is the product of 9 and 5.To understand the Cartesian product of sets, one must first be familiar with basic set operations such as union and intersection, which are appli 7 min read Relations and FunctionsRelations and FunctionsIn mathematics, we often deal with sets of numbers or objects and the ways they are connected. Two important concepts that help us describe these connections are relations and functions.A relation is simply a connection between two sets of objects. Think of it as a rule that pairs elements from one 3 min read Intoduction to Functions | Representation | Types | ExamplesA function is a special relation or method connecting each member of set A to a unique member of set B via a defined relation. Set A is called the domain and set B is called the co-domain of the function. A function in mathematics from set A to set B is defined as,f = {(a,b)| ∀ a ∈ A, b ∈ B}A functi 14 min read Types of FunctionsFunctions are defined as the relations which give a particular output for a particular input value. A function has a domain and codomain (range). f(x) usually denotes a function where x is the input of the function. In general, a function is written as y = f(x).A function is a relation between two s 15 min read Composite functions - Relations and functionsLet f : A->B and g : B->C be two functions. Then the composition of f and g, denoted by g o f, is defined as the function g o f : A->C given by g o f (x) = g{f(x)}, ∀ x ∈ A. Clearly, dom(g o f) = dom(f). Also, g o f is defined only when range(f) is a subset of dom(g). Evaluating composite f 5 min read Invertible FunctionsAs the name suggests Invertible means "inverse", and Invertible function means the inverse of the function. Invertible functions, in the most general sense, are functions that "reverse" each other. For example, if f takes a to b, then the inverse, f-1, must take b to a. Table of ContentInvertible Fu 15 min read Composition of FunctionsThe composition of functions is a process where you combine two functions into a new function. Specifically, it involves applying one function to the result of another function. In simpler terms, the output of one function becomes the input for the other function.Mathematically, the composition of t 11 min read Inverse Functions | Definition, Condition for Inverse and ExamplesInverse Functions are an important concept in mathematics. An inverse function basically reverses the effect of the original function. If you apply a function to a number and then apply its inverse, you get back the original number. For example, if a function turns 2 into 5, the inverse function wil 7 min read Verifying Inverse Functions by CompositionA function can be seen as a mathematical formula or a machine that throws output when an input is given. The output is usually some processed version of the input. Function's inverses can be seen as the operations which give us the input back on giving them the output. In other words, inverse functi 5 min read Domain and Range of a FunctionIn mathematics, a function represents a relationship between a set of inputs and their corresponding outputs. Functions are fundamental in various fields, from algebra to calculus and beyond, as they help model relationships and solve real-world problems.A function represents a relationship between 15 min read Piecewise FunctionPiecewise Function is a function that behaves differently for different types of input. As we know a function is a mathematical object which associates each input with exactly one output. For example: If a function takes on any input and gives the output as 3. It can be represented mathematically as 11 min read Like