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🧩 Factorisation Power Lab ✨

Break algebraic expressions into factors with Class 8 practice on common factors, regrouping and identities.

6x + 12COMMON FACTOR

x² + 5x + 6QUADRATIC

a² − b²IDENTITY

(x + 3)(x + 2)FACTORS

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🧩 Class 8 Factorisation Worksheet

50 Questions

🚀 Start a New Test first! Answer boxes are locked until the test begins. Show Answer remains locked until you check the question.

💡 Quick Tip: First look for a common factor. Then check whether an identity or grouping method makes the expression easier to factor.

ax + ayCOMMON FACTOR

(a+b)²IDENTITY

a²−b²DIFFERENCE

px+pyGROUPING

(x+a)(x+b)TRINOMIAL

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Factorisation for Class 8 Online Practice Worksheet

Class 8 Factorisation Worksheet Free Online: Improve Class 8 Mathematics skills with DigiSadhan's interactive Factorisation Online Practice Worksheet. This free resource gives students fresh practice on taking common factors, factorising by regrouping, using algebraic identities and factorising simple quadratic trinomials. Generate up to 1,000 unique questions for homework, revision, tuition, classroom practice and exam preparation. Choose Foundation, Class 8 Core, Challenge or Mixed difficulty and focus on Common Factor, Regrouping, Algebraic Identities or Quadratic Trinomials. Each question has an answer textbox and Check Answer button. Correct answers turn green with a positive animation and sound, while incorrect answers turn red with a retry animation and sound. The Show Answer button is locked until the learner checks the question, encouraging independent problem solving. The complete answer key remains locked until the test is completed. A live score, checked counter and progress bar make improvement easy to track. Choose No Timer or a 5, 10, 15, 30 or 60-minute test. Download the generated worksheet as a printable PDF. The mobile-first interface is responsive on phones, tablets and desktops. Use this free Class 8 Maths practice tool for CBSE-style revision, assignments, tuition, self-study and exam preparation.

Complete Class 8 Factorisation Practice Guide

What Is Factorisation?

Factorisation is the process of writing an algebraic expression as a product of two or more factors. It is the reverse of expansion. For example, 6x + 12 can be written as 6(x + 2). The factors 6 and (x + 2), when multiplied, give the original expression. Factorisation helps simplify algebra, solve equations and recognise useful patterns.

6x + 12 = 6(x + 2)

Taking a Common Factor

The first method to try is taking out the greatest common factor. Find the largest numerical factor and any variable factor that appears in every term. Divide each term by that common factor and place the remaining expression inside brackets.

ax + ay = a(x + y)

For example, 8x + 20 has a common factor of 4, so it becomes 4(2x + 5). Always multiply the factors back together to verify the result.

Factorisation by Regrouping

Sometimes four terms can be arranged into two groups, with a common factor taken from each group. The aim is to make the same bracket appear twice. That common bracket then becomes one factor.

ax + ay + bx + by = a(x+y) + b(x+y) = (a+b)(x+y)

Using Algebraic Identities

Important identities provide quick factorisation patterns. Recognising the pattern is often faster than trying random factors.

a² + 2ab + b² = (a+b)²

a² − 2ab + b² = (a−b)²

a² − b² = (a+b)(a−b)

For example, x² + 6x + 9 matches a² + 2ab + b² with a = x and b = 3, so it factorises to (x + 3)².

Factorising Quadratic Trinomials

A simple quadratic trinomial can have the form x² + bx + c. Look for two numbers whose product is c and whose sum is b. Those two numbers become the constants in the two brackets.

x² + (p+q)x + pq = (x+p)(x+q)

For x² + 5x + 6, the numbers 2 and 3 multiply to 6 and add to 5. Therefore x² + 5x + 6 = (x + 2)(x + 3).

How to Factorise Step by Step

Write the expression clearly.
Check every term for a common factor.
Take out the greatest common factor if one exists.
Look for a familiar identity such as a² − b² or a perfect-square trinomial.
For a quadratic trinomial, find the required pair of numbers.
Use grouping when there are four suitable terms.
Multiply the final factors to check that they reproduce the original expression.

Common Mistakes to Avoid

Taking out a factor that is not common to every term.
Forgetting the sign of the middle term.
Using the difference-of-squares identity on a sum of squares.
Stopping before the expression is completely factorised.
Choosing numbers with the correct product but incorrect sum in a trinomial.
Not checking the final factors by expansion.
Dropping a negative sign when factoring a negative common factor.

Quick Revision Formula Sheet

ax + ay = a(x+y)

a² + 2ab + b² = (a+b)²

a² − 2ab + b² = (a−b)²

a² − b² = (a+b)(a−b)

x² + (p+q)x + pq = (x+p)(x+q)

ab + ac + db + dc = (a+d)(b+c)

Why Practise Factorisation Online?

Factorisation becomes easier when students see many different forms of the same underlying pattern. Regular practice develops pattern recognition, sign accuracy and confidence with algebraic manipulation. Start with Foundation mode to master common factors, use Class 8 Core for standard school questions and move to Challenge mode for expressions that require more than one step. Shuffle the worksheet to generate fresh numerical combinations rather than memorising answers. If a response is marked wrong, identify the common factor or identity before trying again. Finally, expand your factors to verify the answer. This check is a powerful habit because it connects factorisation directly to multiplication and helps catch small algebraic mistakes.