Class 9 Maths Chapter 4, Exploring Algebraic Identities, teaches the standard identities through pictures and algebra tiles rather than as a list to memorise. It opens with a pattern you can test yourself: take three consecutive squares such as 1, 4 and 9, add the outer two and subtract twice the middle one, and the answer is always 2. The chapter explains why, then uses identities to factorise expressions and simplify rational expressions.
What Class 9 Maths Chapter 4 Covers
4.1 Introduction and 4.2 Visualising Identities build (x + y)² and its relatives as areas of squares and rectangles.
4.3 Factorisation Using Identities and 4.4 More Identities extend to (x + y + z)² and the product (x + a)(x + b), with a geometric reading of each.
4.5 and 4.6 Factorisation With and Without Algebra Tiles factorise quadratic expressions first by arranging tiles into rectangles, then symbolically.
4.7 Finding New Identities covers cubes: (x + y)³, (x – y)³, x³ + y³, x³ – y³ and x³ + y³ + z³ – 3xyz.
4.8 Simplifying Rational Expressions cancels common factors from numerator and denominator, as long as the factor is not zero.
Exercises in Chapter 4
- Exercise Sets 4.1 to 4.5: visualising identities, factorising, expanding cubes, and simplifying rational expressions.
- End-of-Chapter Exercises and a chapter summary that lists every identity studied, from (x + y)² = x² + 2xy + y² to x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx).
Read Class 9 Maths Chapter 4 Online
More Chapters
- Previous: Chapter 3: The World of Numbers
- Next: Chapter 5: I’m Up and Down, and Round and Round
- Hindi medium: Class 9 Maths Chapter 4 PDF in Hindi (बीजीय सर्वसमिकाओं का अन्वेषण)
- All Maths chapters and the other Class 9 books: Class 9 NCERT books 2026-27
- All Class 1 to 12 NCERT Textbooks: NCERT Books PDF (Class 1–12)
FAQ
Which identities are in Class 9 Maths Chapter 4?
(x ± y)², (x + y + z)², (x + y)(x – y), (x + a)(x + b), (ax + b)(cx + d), x³ ± y³, (x ± y)³ and x³ + y³ + z³ – 3xyz.
What are algebra tiles?
Square and rectangular pieces that stand for x², x and 1. Arranging them into a rectangle shows how a quadratic expression factorises, which the chapter uses in section 4.5.