Algebraic Expressions Practice Questions Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Algebraic expressions are fundamental components of algebra that represent quantities and relationships using variables, constants, and operations. They form the basis for solving equations and understanding mathematical relationships.In this article, we will learn what algebraic expressions are and solve problems related to them.What is Algebraic expression?An algebraic expression can be simple or complex and describes a wide range of mathematical phenomena.The algebraic expression does not contain an equality sign. It simply represents a value that can be calculated or simplified based on the variables' values.Example:5x + 32x2 - 4x + 1\frac{2x^2 + 3x - 5}{x - 1} \sqrt{x^2 + 4}, etc.Distributive PropertyDistributive property allows you to eliminate parentheses by distributing multiplication over addition or subtraction within the parentheses.Formula: a(b+c) = ab + ac Combining Like TermsCombine terms with the same variable to simplify the equation.Formula: ax + bx = (a+b)xImportant ConceptsAlgebraic expression contains:Variables: Symbols (such as x, y, z) that represent unknown values or quantities.Constants: Fixed numerical values (such as 1, -5, 2.3) that do not change.Operators: Symbols that indicate operations to be performed, including addition (+), subtraction (-), multiplication (× or ·), and division (÷ or /).Exponents: Powers to which variables are raised (such as x2 or y3).How to Solve Algebraic ExpressionTo solve practice questions follow the steps added below:Step 1: Identify Terms then combine them together.Step 2: Distribute and CombineStep 3: Identify Common FactorsStep 4: Isolate the VariableStep 5: Simplify the resultsAlgebraic Expressions Practice Questions Question 1: Simplify Algebraic Expression: 4(a+3) -2(2a-5) + 3(a+1).Solution:Distribute the 4, -2, and 3, then combine like terms. = 4a + 12 - 4a + 10 + 3a + 3= 3a + 25 Question 2: Simplify Algebraic Expression: 7x+4x.Solution:= 7x + 4x= 11xQuestion 3: Simplify Algebraic Expression: 3(x+2)+4xSolution:= 3(x+2) + 4x= 3x + 6 + 4x= 7x + 6Question 4: Simplify Algebraic Expression: \frac{5x^2 - 3x + 2}{x^2 + 2x + 1}Solution:Factor denominator x2 + 2x + 1Recognize that x2 + 2x + 1 = (x+1)2So, we have:\frac{5x^2 - 3x + 2}{(x + 1)^2}Numerator 5x2- 3x + 2 cannot be easily factored further in a way that will cancel out with the denominator. Therefore, this fraction is already in its simplest form.Question 5: Simplify Algeabric Expression: -2(3y-4)Solution:= -2(3y-4)= -6y+8Question 6: Simplify Algeabric Expression: 5a-3+2a+7Solution:= 5a + 2a - 3 + 7= 7a + 4Question 7: Simplify Algeabric Expression: \frac{(x - 1)^2}{x^2 - 2x + 1} + \frac{(x + 1)^2}{x^2 + 2x + 1}Solution:Simplify Each Term:\frac{(x - 1)^2}{x^2 - 2x + 1}Notice that x2 - 2x + 1 = (x - 1)2=\frac{(x - 1)^2}{(x - 1)^2} = 1Simplify Second Term:\frac{(x + 1)^2}{x^2 + 2x + 1}Notice that x2 + 2x + 1 = (x+1)2\frac{(x + 1)^2}{(x + 1)^2} = 1Add simplified terms: 1 + 1 = 2Hence \frac{(x - 1)^2}{x^2 - 2x + 1} + \frac{(x + 1)^2}{x^2 + 2x + 1} = 2Question 8: Simplify Algeabric Expression: \frac{5x}{4} + \frac{3x}{4}Solution:= 5x/4 + 3x/4Taking LCM of Denominator= (5x + 3x)/4= 8x/4 = 2xQuestion 9: Simplify Algebraic Expression: 2x2+3x-4+x2-2x+1Solution:= 2x2 + x2+ 3x - 2x - 4 + 1= 3x2 + x - 3Question 10: Simplify Algebraic Expression: 2(x+3)-(x-4)+5(x+1)Solution:= 2(x+3) - (x-4) + 5(x+1)= 2x + 6 - x + 4 + 5x + 5= 6x + 15Algebraic Expressions: Practice ProblemsP 1: Solve the algebraic equation: \frac{4x^2 - 9}{2x - 3} \cdot \frac{3x + 3}{x^2 - 1}P 2: Solve the algebraic equation: \frac{2x^2 - 8}{4x} + \frac{3x^2 + 6x}{2x}P 3: Solve the algebraic equation: 7x+4x+2x+4y-2y+9x.P 4: Solve the algebraic equation: \frac{5x - 7}{x + 2} - \frac{3x + 1}{x + 2}P 5: Solve the algebraic equation: -2(3x-6)P 6: Solve the algebraic equation: \frac{2x^3 - 6x^2 + 4x}{2x}P 7: Solve the algebraic equation: \frac{6x^2 - 5x - 6}{x^2 - 3x}P 8: Solve the algebraic equation: \frac{3x^2 - 5x + 2}{x^2 - x - 2}P 9: Solve the algebraic equation: 9a-2a+74a - 6aP 10: Solve the algebraic equation: \frac{x^2 + 2x + 1}{x^2 - 1} + \frac{x^2 - 1}{x^2 + 2x + 1}Also Check,Are algebraic expressions polynomials?Practice questions on Rational numbers Comment More infoAdvertise with us Next Article What are Numbers? A ashishtiwa2irm Follow Improve Article Tags : Mathematics School Learning Practice Questions Similar Reads Maths Mathematics, often referred to as "math" for short. It is the study of numbers, quantities, shapes, structures, patterns, and relationships. It is a fundamental subject that explores the logical reasoning and systematic approach to solving problems. Mathematics is used extensively in various fields 5 min read Basic ArithmeticWhat are Numbers?Numbers are symbols we use to count, measure, and describe things. They are everywhere in our daily lives and help us understand and organize the world.Numbers are like tools that help us:Count how many things there are (e.g., 1 apple, 3 pencils).Measure things (e.g., 5 meters, 10 kilograms).Show or 15+ min read Arithmetic OperationsArithmetic Operations are the basic mathematical operations—Addition, Subtraction, Multiplication, and Division—used for calculations. These operations form the foundation of mathematics and are essential in daily life, such as sharing items, calculating bills, solving time and work problems, and in 9 min read Fractions - Definition, Types and ExamplesFractions are numerical expressions used to represent parts of a whole or ratios between quantities. They consist of a numerator (the top number), indicating how many parts are considered, and a denominator (the bottom number), showing the total number of equal parts the whole is divided into. For E 7 min read What are Decimals?Decimals are numbers that use a decimal point to separate the whole number part from the fractional part. This system helps represent values between whole numbers, making it easier to express and measure smaller quantities. Each digit after the decimal point represents a specific place value, like t 10 min read ExponentsExponents are a way to show that a number (base) is multiplied by itself many times. 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So, if you ch 5 min read Polynomials| 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 CoefficientA coefficient is a number that multiplies a variable in a mathematical expression. It tells you how much of that variable you have. For example, in the term 5x, the coefficient is 5 — it means 5 times the variable x.Coefficients can be positive, negative, or zero. Algebraic EquationA coefficient is 8 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. 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The solutions provided by GeeksforGeeks help to practice the qu 5 min read RD Sharma Class 9 SolutionsRD Sharma Solutions for class 9 provides vast knowledge about the concepts through the chapter-wise solutions. These solutions help to solve problems of higher difficulty and to ensure students have a good practice of all types of questions that can be framed in the examination. Referring to the sol 10 min read RD Sharma Class 10 SolutionsRD Sharma Class 10 Solutions offer excellent reference material for students, enabling them to develop a firm understanding of the concepts covered. in each chapter of the textbook. As Class 10 mathematics is categorized into various crucial topics such as Algebra, Geometry, and Trigonometry, which 9 min read RD Sharma Class 11 Solutions for MathsRD Sharma Solutions for Class 11 covers different types of questions with varying difficulty levels. Practising these questions with solutions may ensure that students can do a good practice of all types of questions that can be framed in the examination. This ensures that they excel in their final 13 min read RD Sharma Class 12 Solutions for MathsRD Sharma Solutions for class 12 provide solutions to a wide range of questions with a varying difficulty level. With the help of numerous sums and examples, it helps the student to understand and clear the chapter thoroughly. Solving the given questions inside each chapter of RD Sharma will allow t 13 min read Like