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Tamil Nadu (TNBSE)Class 8 Mathematics★ 8-12 marks in the TN Class 8 annual exam through MCQs, identities, factorisation and equation problems

Algebra

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 3, Algebra. Multiplication and division of algebraic expressions, algebraic identities (including cubic identities), factorisation, and linear equations in one variable. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

⏱ 22 min readMedium difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Multiply and divide algebraic expressions
2Apply algebraic and cubic identities
3Factorise expressions using several methods
4Solve linear equations in one variable
5Use identities to expand quickly

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Why this chapter matters

Algebra teaches how to operate on expressions, use identities and solve equations — core skills tested heavily in the TN Class 8 exam and the foundation for Class 9 and 10 algebra.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 7 — Algebraic expressions

Terms, coefficients and simple identities.

Algebra — Class 8 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 8 Mathematics, Chapter 3. Operating on expressions, identities and equations.

1. About this chapter

This chapter covers multiplication and division of algebraic expressions, identities (including cubic ones), factorisation, and linear equations in one variable.

2. Operations on expressions

Multiplication: monomial × monomial, monomial × binomial, binomial × binomial (use the distributive law).
Division: divide each term of the dividend by the divisor; cancel common factors.

3. Identities

(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
(a + b)(a − b) = a² − b²
(x + a)(x + b) = x² + (a + b)x + ab
Cubic: (a + b)³ = a³ + 3a²b + 3ab² + b³; (a − b)³ = a³ − 3a²b + 3ab² − b³.

4. Factorisation and equations

Factorisation methods: common factor, grouping, identities, and splitting the middle term.
Linear equation in one variable: solve by isolating the variable, e.g. 2x + 3 = 11 → x = 4.

5. Worked examples

Example 1. Multiply (x + 2)(x + 5). = x² + (2 + 5)x + (2)(5) = x² + 7x + 10.

Example 2. Factorise x² − 16. = (x + 4)(x − 4).

Example 3. Solve 3x − 7 = 8. 3x = 15 → x = 5.

6. Common mistakes

Mistake: Forgetting the middle term in (a + b)². Fix: (a + b)² = a² + 2ab + b².
Mistake: Dividing only the first term of an expression. Fix: Divide each term by the divisor.
Mistake: Changing the sign incorrectly when moving a term. Fix: Moving a term across "=" reverses its sign.

7. Practice (book-back style)

Multiply 3x(2x + 5).
Expand (2x − 3)².
Factorise x² − 9.
Solve 5x + 2 = 17.
Expand (a + b)³.

8. Answer key

6x² + 15x.
4x² − 12x + 9.
(x + 3)(x − 3).
5x = 15 → x = 3.
a³ + 3a²b + 3ab² + b³.

9. Quick revision

Chapter 3 · expressions, identities, factorisation, equations.
Multiply using distributive law; divide each term.
(a ± b)² = a² ± 2ab + b²; (a + b)(a − b) = a² − b².
(a + b)³ = a³ + 3a²b + 3ab² + b³.
Solve linear equations by isolating the variable (sign flips across =).

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Square identities

(a ± b)² = a² ± 2ab + b²

Watch the middle term.

Difference of squares

(a + b)(a − b) = a² − b²

Common factorisation.

Product identity

(x + a)(x + b) = x² + (a + b)x + ab

Quick expansion.

Cubic identity

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a − b)³ has alternating signs.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Forgetting the middle term in (a + b)²

✓ (a + b)² = a² + 2ab + b².

WATCH OUT

✗ Dividing only the first term of an expression

✓ Divide each term by the divisor.

WATCH OUT

✗ Wrong sign when moving a term

✓ Moving a term across '=' reverses its sign.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiple choice questions

MCQs on identities, factorisation and equations.

Questions

Identities / multiplication

Expand and multiply expressions.

Questions

Factorisation / equations

Factorise and solve linear equations.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Multiply

Multiply 3x(2x + 5).

▶ Show solution

6x² + 15x.

Q2EASY· Identity

Expand (2x − 3)².

▶ Show solution

4x² − 12x + 9.

Q3EASY· Factorise

Factorise x² − 9.

▶ Show solution

(x + 3)(x − 3).

Q4EASY· Equation

Solve 5x + 2 = 17.

▶ Show solution

5x = 15 → x = 3.

Q5MEDIUM· Identity

Multiply (x + 2)(x + 5).

▶ Show solution

x² + 7x + 10.

Q6EASY· Identity

Expand (a + b)³.

▶ Show solution

a³ + 3a²b + 3ab² + b³.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Chapter 3 of Samacheer Kalvi Class 8 Mathematics.
•Multiply via distributive law; divide each term.
•(a ± b)² = a² ± 2ab + b²; (a + b)(a − b) = a² − b².
•(x + a)(x + b) = x² + (a + b)x + ab.
•(a + b)³ = a³ + 3a²b + 3ab² + b³.
•Solve linear equations by isolating the variable (sign flips across =).

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 8-12 marks across MCQ, identity, factorisation and equation problems

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Identities and factorisation
Short Answer	2-3	2-3	Expand, multiply, factorise
Equations	2-3	1	Linear equations

Prep strategy

Memorise the standard and cubic identities
Practise multiplication and division of expressions
Drill factorisation methods
Solve linear equations carefully with sign rules

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Problem solving

Linear equations model everyday word problems.

Geometry

Identities simplify area and length expressions.

Coding and logic

Algebraic manipulation underlies formulas in programs.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Pick the right identity for expansion
Divide every term, not just the first
Flip signs when moving terms
Check the solution by substitution

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Factorise a cubic using grouping.
Use identities to evaluate 102² mentally.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 8 Annual ExamHigh

Foundation / NMMS MathematicsMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

They give ready-made results for common products, so you can expand expressions like (a + b)² or (a + b)³ in one step instead of multiplying term by term.

Bring all variable terms to one side and constants to the other (remembering signs flip across the equals sign), then divide to isolate the variable.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 8 mock tests

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