NCERT Solutions for Class 9th Maths Chapter 4 Exploring Algebraic Identities
Updated on 2026-09-08
About this chapter
An equation such as x² − 1 = 24 holds only for x = 5 or x = −5; an identity such as (x + y)² = x² + 2xy + y² holds for every value of x and y. That is the whole difference. A square of side (a + b) cuts into a², b² and two ab rectangles, so (a + b)² = a² + 2ab + b². Replacing b by −b — legitimate, because an identity is true for all values — gives (a − b)² = a² − 2ab + b². A square of side (a + b + c) cuts into nine pieces and gives the three-letter version. Read backwards, every identity is a factorisation rule. Recognising a² + 2ab + b² inside 9x² + 24xy + 16y² is what lets you write it as (3x + 4y)². Algebra tiles turn factorising x² + 7x + 12 into a jigsaw: the only split of 7x that makes the unit tiles fill a rectangle is 3x + 4x, because 3 + 4 = 7 and 3 × 4 = 12. Without tiles this i
- Introduction
- Visualising Identities
- Factorisation of Algebraic Expressions Using Identities
- More Identities
- Factorisation Using Algebra Tiles
- Factorisation Without Using Algebra Tiles
- Finding New Identities
- Simplifying Rational Expressions
- Chapter 4 Exploring Algebraic Identities
Exercises
- Think and Reflect — Introduction Page 69
- Think and Reflect — Visualising Identities Page 71
- Exercise Set 4.1 — Visualising Identities Page 71–72
- Think and Reflect — Factorisation of Algebraic Expressions Using Identities Page 73
- Exercise Set 4.2 — Factorisation of Algebraic Expressions Using Identities Page 74–75
- Think and Reflect — More Identities Page 76
- Exercise Set 4.3 — More Identities Page 76–77
- In-text Questions — More Identities Page 77
- Think and Reflect — More Identities Page 78
- Think and Reflect — Factorisation Using Algebra Tiles Page 79
- Think and Reflect — Factorisation Using Algebra Tiles Page 79
- Think and Reflect — Factorisation Using Algebra Tiles Page 80
- In-text Questions — Factorisation Using Algebra Tiles Page 80
- Exercise Set 4.4 — Factorisation Without Using Algebra Tiles Page 81–82
- Think and Reflect — Factorisation Without Using Algebra Tiles Page 82
- In-text Questions — Finding New Identities Page 85
- Think and Reflect — Finding New Identities Page 85
- Think and Reflect — Simplifying Rational Expressions Page 87
- Exercise Set 4.5 — Simplifying Rational Expressions Page 87
- Chapter 4 Exploring Algebraic Identities — End-of-Chapter Exercises Page 88–90