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A Special Identity
Last updated at May 18, 2026 by Teachoo
Class 9
Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)
- Consecutive Square Numbers
- Visualising Algebraic Identities
- Exercise Set 4.1
- Factorisation of Algebraic Expressions Using Identities
- Exercise Set 4.2
- More Identities
- Exercise Set 4.3
- Rewriting a2 - b2 Identity
- Factorisation Using Algebra Tiles
- Factorisation by Splitting the Middle term
- Exercise Set 4.4
-
Finding New Algebraic Identities
- Simplifying Rational Expressions
- Exercise Set 4.5
- Word Problems
- End-of-Chapter Exercises
Transcript
A Special Identity We have a special cube formula (x+y+z)(x^2+y^2+z^2-xy-xz-yz)=x^3+y^3+z^3-3xyz Formula Breakdown and Factors: SUM OF THE VARIABLES (LINEAR FACTOR) THE INDIVIDUAL CUBES CYCLIC QUADRATIC FACTOR The factors of x^3+y^3+z^3-3xyz are: The Linear Sum (x+y+z) The Cyclic Quadratic Trinomial (x^2+y^2+z^2-xy-xz-yz) Special case If x + y + z = 0, then x3 + y3 + z3 = 3xyz
