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Algebraic Expressions

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Mastering Algebraic Expressions: Understanding Algebraic Terms and Simple Expressions

Comprehensive Definition, Description, Examples & Rules 

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What are Algebraic Expressions?

Algebraic expressions are a mathematical term consisting of constants, variables, and algebraic operations. It is a mathematical statement with a number, a variable, and an arithmetic operation between them. 

The components of algebraic expression are:

Variables

The primary component of algebraic expressions is a variable. The variable is a letter that always represents an unknown number. It carries a value written in an expression and is usually assigned by letters like— x, y, and z. 

Constant

A constant is a value or a number that does not change in an expression and is always the same in all situations. The data item has a predefined value, and its value never changes and does not consist of a variable.

The examples to illustrate simple algebraic expressions are:

  • 2x² + 4y + 26 (‘x²’ and ‘y’ are variables while ’26’ is constant and ‘2’ and ‘4’ are coefficients of the variable)

Key Concepts of Algebra

Algebra is a type of mathematics in which you must use symbols and letters that typically represent unknown numbers. It is the study of variables and follows specific rules to manipulate the variables into different formulas. 

Algebra helps solve all mathematical equations to discover unknown quantities in the real world. The specific real-life areas where you have to use algebra are:

  • Calculate Bank Interest
  • Finding Percentages

You can use these to represent mathematics and relationships by including variable numbers and operators. For the numbers that you don’t know and are unknown, you have to use variables that help you explain the relationship between these values. By forming this relationship, you can solve that algebraic expression and find the exact value of the variables present in that expression. 

The importance of Algebraic terms in Algebraic expressions are:

  • Algebraic terms play an important role in forming an expression of algebra.
  • The algebraic terms and expressions are connected through arithmetic operations, making calculations easy.
  • Algebraic terms help in simplification and solving the equation faster. 

Algebraic Terms

An algebraic term is a particular data that can be represented as a number or a variable. You can state an algebraic term as a product of two or more variables or a product of a variable and a number. You form an algebraic expression by joining the algebraic terms.

The examples of the algebraic terms are:

  • Variables
  • Constant
  • Coefficients

There is a basic difference between all these algebraic terms. Constant is a term that is an expression that only includes numbers, and the values can never change. 

A variable is a value represented in letters, which can always change. The letters of the variable represent the form of unknown numbers. 

While on the other hand, a coefficient of a variable is a number written along with the variable in the term. 

Examples of algebraic expressions are:

4x + 5y – 33

  • ‘x’ and ‘y’ are variables
  • 33 is constant
  • ‘4’ and ‘5’ are the coefficients of variables

Types of Algebraic Expressions

The types are:

Binomial

It is a mathematical expression that has two groups of numbers. You can join these variables with arithmetic operations (+ or -). It is the sum of two terms, each of which is a single monomial.

  • 3x² + 2y³

 ‘x’ and ‘y’ are variables, while ‘3’ and ‘2’ are coefficients, and powers are ‘2’ and ‘3’. These two are single binomials. 

Polynomial

It has more than two algebraic terms and is a sum of several terms with powers of a similar variable. It consists of nearly all the components of an algebraic expression, especially coefficients and interlaminates.

  • 5x + 8y + 90

’90’ is constant, ‘5′ and ‘8’ are coefficients, , and’ x’ and ‘y’ are variables.

Monomial

It is a type of algebraic expression that consists of only a single term. It is an algebraic expression that consists of a single term but can have multiple variables.

  • 3x²y

‘3’ is the coefficient, ‘x’ and ‘y’ are variables, and’ 2′ is the degree of monomial.

Simple Algebraic Expressions

It is an expression created with constant algebraic numbers and variables with algebraic operations. A simple algebraic operation consists of all these terms, and you can form this equation effectively. Examples of simple algebraic expressions are:

  • 5x² + 3xy + 72

Here, ‘5’ and ‘3’ are coefficients, ‘x’ and ‘xy’ are variables, and ’72’ is constant.

You can evaluate an algebraic expression to find out the exact value of the expression by replacing the variable with a given number. For evaluating an algebraic expression, you have to substitute a given number with the variable and find out the exact value of the variable to find out the result of the overall expression.

The practical examples of how you can use the simple algebraic expressions in daily life are:

  • Calculating run rate in a cricket match.
  • Find out the total expenses in grocery by calculating it in algebraic expressions.
  • Calculating the travelling distance of a bike.

Operations with Algebraic Expressions

There are many common arithmetic operations that you can use in algebraic expressions. These are:

Addition

It is the simple way of using the ‘+’ symbol as an algebraic operation where you can add the variable coefficient and constant of the sentence.

The example is: x + y + 8 (‘x’ and ‘y’ are variables while ‘8’ is constant)

Subtraction

It is the simple way of using the ‘-‘ symbol as an algebraic operation where you can subtract the variables’ coefficients and the expression’s constant. In situations, you can use both the addition and the subtraction operations as well. 

An example of subtraction operations is y – 89 (‘y’ is a variable, and ’89’ is a constant.

Multiplication

It is when you want to multiply all the algebraic terms of the expressions and form an algebraic expression, or you can use the multiplication and the addition or subtraction symbols together. 

The example is 3x – 9 (‘3’ is the coefficient multiplied by variable ‘x’ and ‘9’ is the constant)

Division

It is the algebraic operation you use to divide the algebraic terms or the already created monomials of the expression. 

The example is x/ 6 (‘x’ is the variable being divided by the constant ‘6’)

Steps to Use these Algebraic Expressions:

  • For the addition expression, you have to add all your variables and constants and get your final expression.
  • For subtraction, you have to subtract the variable and the constant.
  • You can use both addition and subtraction together.
  • You must join the expression with addition or subtraction for multiplication or division.
  • You can also singularly use multiplication or division expressions. 

Real-Life Applications

Algebraic expressions have a huge part in practical applications such as:

  • Science: Calculating the algebraic expression to finalize the scientific calculations, especially the measurements of the distance from the Earth to the sun, requires algebraic calculation. 
  • Engineering: The Engineers primarily use algebraic expressions in all calculations while making bridges and buildings.
  • Finance: The financial department has to calculate a lot about algebraic expressions as it is important in calculating bank interest and interest on loans. 

Real-Life examples:

  • Calculation of the Economy of a country.
  • Total expenses of a company
  • Calculating revenue cost

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Key Takeaways

  1. Algebraic equations are important for science and engineering knowledge in real life.

  2. Calculating the algebraic expression in simplified form is easy by following the BODMAS rule.

  3. Various algebraic terms form an algebraic expression, and keeping all in mind is very important.

  4. There are different types of algebraic expressions according to different rules.

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Frequently Asked Questions

You need to follow specific steps which will help you calculate and simplify an algebraic expression. These are:

  • Solve the brackets first by subtracting or adding the terms.
  • Use the exponent rule if the equation uses the exponents in it.
  • Follow BODMAS rule

An algebraic expression consists of a number, a variable, or a combination of variables and the numbers with the constant. On the other hand, an equation is a combination of two expressions that you can connect with an equal sign.

The basic operations of an algebraic expression are:

  • Addition
  • Subtraction
  • Multiplication
  • Division

The application of algebraic expression in different fields are:

  • In mathematics, you can solve complex equations.
  • You can use algebraic expressions for computer programming and Python.
  • You can use algebraic expressions to calculate a country’s economy or a company’s revenue cost.
  • In the finance sector, you can use it to calculate interest rates. 
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2D Shapes2cosacosb Formula30-60-90 Formulas3D ShapesAbsolute Value FormulaAcute AngleAcute Angle triangleAdditionAlgebra FormulasAlgebra of MatricesAlgebraic EquationsAlgebraic ExpressionsAngle FormulaAnnulusAnova FormulaAnti-derivative FormulaAntiderivative FormulaApplication of DerivativesApplications of IntegrationArc Length FormulaArccot FormulaArctan FormulaArea Formula for QuadrilateralsArea FormulasArea Of A Sector Of A Circle FormulaArea Of An Octagon FormulaArea Of Isosceles TriangleArea Of ShapesArea Under the Curve FormulaArea of RectangleArea of Regular Polygon FormulaArea of TriangleArea of a Circle FormulaArea of a Pentagon FormulaArea of a Square FormulaArea of a Trapezoid FormulaArithmetic Mean FormulaArithmetic ProgressionsArithmetic Sequence Recursive FormulaArithmetic and Geometric ProgressionAscending OrderAssociative Property FormulaAsymptote FormulaAverage Deviation FormulaAverage Rate of Change FormulaAveragesAxioms Of ProbabilityAxis of Symmetry FormulaBasic Math FormulasBasics Of AlgebraBinary FormulaBinomial Probability FormulaBinomial Theorem FormulaBinomial distributionBodmas RuleBoolean AlgebraBusiness MathematicsCalculusCelsius FormulaCentral Angle of a Circle FormulaCentral Limit Theorem FormulaCentroid of a Trapezoid FormulaChain RuleChain Rule FormulaChange of Base FormulaChi Square FormulaCirclesCircumference FormulaCoefficient of Determination FormulaCoefficient of Variation FormulaCofactor FormulaComplete the square formulaComplex numbersCompound Interest FormulaConditional Probability FormulaConeConfidence Interval FormulaCongruence of TrianglesCorrelation Coefficient FormulaCos Double Angle FormulaCos Square theta FormulaCos Theta FormulaCosec Cot FormulaCosecant FormulaCosine FormulaCovariance FormulaCubeCurated Maths Resources for Teachers – EdulyteCylinderDecimalsDifferential calculusDiscover the world of MathsEllipseEquilateral triangleEuler’s formulaEven numbersExponentsFractionFraction to decimalGeometric sequenceHeptagonHyperbolaIntegersIntegrationIntegration by partsLinesLocusMatricesNatural numbersNumber lineOdd numbersParallelogramPercentage formulaPerimeterPolygonPolynomialsPrismProbabilityPyramidPythagoras theoremRoman NumeralsScalene triangleSetsShapes NamesSimple interest formulaSlope formulaSolid shapesSphereSquareStandard deviation formulaSubtractionSymmetryTimeTrianglesTrigonometry formulaTypes of anglesValue of PiVariance formulaVectorVolume formulasVolume of a coneVolume of sphere formulaWhole numbers
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