Chapter 4 — Exploring Algebraic Identities

Chapter 4 of NCERT Class 9 Maths, "Exploring Algebraic Identities", introduces algebraic identities such as (a+b)^2 = a^2 + 2ab + b^2, visualises them with geometric models and algebra tiles, and uses them to expand, factorise, simplify rational expressions, and speed up calculations.

This chapter explores algebraic identities, special rules true for all values of their variables, and distinguishes an identity from an ordinary equation. It revisits (a+b)^2, (a-b)^2, and (a+b+c)^2, visualising them with squares, rectangles, and a cube, then verifies them using the distributive property. The chapter uses these identities to expand binomials, evaluate squares like 43^2 and 119^2, and factorise expressions. It introduces cube identities (a+b)^3 and (a-b)^3, the differences/sums of cubes x^3-y^3 and x^3+y^3, the identity x^3+y^3+z^3-3xyz, factorisation with algebra tiles by splitting the middle term, and simplifying rational expressions through factorisation.

1. 01Identity (a+b)^2 = a^2 + 2ab + b^2 and (a-b)^2 = a^2 - 2ab + b^2
2. 02An identity is true for all values; an equation need not be
3. 03Three-term square: (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
4. 04Difference of squares: a^2 - b^2 = (a+b)(a-b)
5. 05Cube identities (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 and (a-b)^3
6. 06x^3 - y^3 = (x-y)(x^2+xy+y^2) and the x^3+y^3+z^3-3xyz identity
7. 07Factorising quadratics by splitting the middle term and using algebra tiles