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Algebraic Expressions and Identities in One Variable for Class 8 Online Practice Worksheet

Class 8 Algebraic Expressions and Identities Worksheet Free Online: Build strong algebra skills with DigiSadhan's interactive Algebraic Expressions and Identities Online Practice Worksheet for Class 8 Mathematics. This free practice tool gives students fresh questions on variables, constants, coefficients, terms, like and unlike terms, simplification, distributive property, evaluation of expressions and important algebraic identities. Generate up to 1,000 questions for revision, homework, tuition, classroom practice and exam preparation. Select Foundation, Class 8 Core, Challenge or Mixed difficulty and choose a specific topic or a complete mixed worksheet. Every question includes an answer box and a Check Answer button. Correct answers turn the textbox green and trigger a positive animation and sound; incorrect answers turn it red and trigger a retry animation and sound. Students cannot reveal an answer before attempting and checking the question. After checking, the Show Answer button becomes available for that question, while the complete answer key remains locked until the test is completed. A live progress bar, score counter and checked-question counter make practice measurable. Choose No Timer or a 5, 10, 15, 30 or 60-minute timed test. When the test is completed, the tool calculates the score and percentage and unlocks the complete answer key. A PDF download option creates a printable copy of the generated worksheet. The responsive mobile-first design works on smartphones, tablets and desktops. Student-friendly algebra graphics keep the practice approachable while dynamically generated numerical values make repeated tests different. This tool is useful for Class 8 Maths revision, CBSE-style preparation, school assignments, tutoring, remedial practice and independent learning.

Complete Class 8 Algebraic Expressions and Identities Practice Guide

What Is an Algebraic Expression?

An algebraic expression combines numbers, variables and mathematical operations. In an expression such as 5x + 7, x is the variable, 5 is its coefficient and 7 is the constant. A term is a part separated by a plus or minus sign. Learning to identify these parts is the first step toward simplifying and evaluating expressions.

Variables, Constants and Coefficients

A variable represents an unknown or changeable number. A constant has a fixed value. The numerical factor multiplying a variable is called its coefficient. In −8x, the coefficient is −8. If a variable appears without a visible number, its coefficient is 1; therefore x means 1x and −x means −1x.

Like and Unlike Terms

Like terms have exactly the same variables raised to the same powers. For example, 3x and −7x are like terms, while 3x and 3y are unlike terms. Only like terms can be combined by addition or subtraction. This rule prevents many common simplification errors.

Simplifying Expressions

To simplify an expression, first remove brackets where necessary, then collect like terms. Keep every sign attached to the correct term. For example, 4x + 3 − 2x + 5 becomes 2x + 8 because 4x − 2x = 2x and 3 + 5 = 8.

Distributive Property

The distributive property tells us that a factor outside a bracket multiplies every term inside the bracket. It is especially useful for expanding expressions and removing brackets.

Important Algebraic Identities

An identity is an equality that remains true for every permitted value of its variables. Class 8 students should become familiar with the square identities because they make expansion and calculation faster.

Using Identities to Calculate Quickly

Identities can turn difficult multiplication into simple addition and subtraction. For example, 49² can be viewed as (50 − 1)². Using the second identity gives 2500 − 100 + 1 = 2401. The important skill is recognising a convenient nearby number.

Evaluating an Expression

To evaluate an expression, substitute the given value for the variable and follow the order of operations. Use brackets when substituting a negative number. For example, if x = −3, then 2x + 5 becomes 2(−3) + 5 = −1.

Multiplication of Algebraic Terms

When multiplying algebraic terms, multiply the numerical coefficients and then multiply the variable parts. For the same variable, exponents are added. At Class 8 level, this is often seen in products such as 3x × 4x = 12x².

How to Solve Algebra Questions

1. Read the expression carefully.
2. Identify variables, coefficients, constants and terms.
3. Look for brackets and signs.
4. Use the distributive property when required.
5. Combine only like terms.
6. For identities, match the expression to the correct formula.
7. Substitute values carefully when evaluating.
8. Check the result by expanding or substituting a simple value.

Common Mistakes to Avoid

• Combining unlike terms such as 3x + 4y.
• Dropping a negative sign when removing brackets.
• Multiplying only the first term instead of every term inside brackets.
• Forgetting the middle term 2ab in (a+b)².
• Writing (a−b)² as a²−b² instead of a²−2ab+b².
• Confusing an expression with an equation or identity.
• Forgetting that x means 1x.
• Substituting a negative value without brackets.

Quick Formula Sheet

Regular practice develops algebraic fluency. Start with Foundation mode to master terms and coefficients, use Core mode for Class 8 applications, and move to Challenge mode for multi-step identities and simplification. Shuffle the worksheet to generate fresh values and avoid memorising answers. When a response is marked wrong, inspect the signs and identify whether the mistake came from combining unlike terms, distributing incorrectly, selecting the wrong identity or substituting a value incorrectly. Use the timer for exam-style practice and the final answer key for structured revision. Algebra becomes easier when each step is written clearly rather than calculated mentally.