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Identity VIII
Identities VIII You are here
Ex 2.4, 9 (i)
Ex 2.4, 10 (i) Important Deleted for CBSE Board 2025 Exams
Ex 2.4,12 Important
Ex 2.4,13
Ex 2.4, 14 (i)
Example 20 Important
Chapter 3 Class 9 Coordinate Geometry→
Chapter 2 Class 9 Polynomials
Concept wise
 Definition
 Value of a polynomial at a given point
 Verifying Zeroes of a polynomial
 Finding Zeroes of a polynomial
 Remainder Theoram
 Check if factor
 Factorisation by middle term
 Factorisation by factor formula
 Factorizing cubic equation
 Identity I  IV
 Identity V

Identity VIII
Last updated at April 16, 2024 by Teachoo
Identity VII is
 a ^{ 3 } + b ^{ 3 } + c ^{ 3 } − 3abc = (a + b + c) (a ^{ 2 } + b ^{ 2 } + c ^{ 2 } − ab − bc − ac)
Lets take an example
a ^{ 3 } + b ^{ 3 } + c ^{ 3 } − 3abc = (a + b + c) (a ^{ 2 } + b ^{ 2 } + c ^{ 2 } − ab − bc − ac)
2 ^{ 3 } + 3 ^{ 3 } + 4 ^{ 3 } – 3(2)(3)(4)
= (2 + 3 + 4) (2 ^{ 2 } + 3 ^{ 2 } + 4 ^{ 2 } – (2)(3) – (3)(4) – (4)(2))
8 + 27 + 64 – 72 = (9) (4 + 9 + 16 – 6 – 12 – 8)
99 – 72 = (9) (29 – 26)
27 = (9) (3)
27 = 27
If a + b + c = 0
Then,
a ^{ 3 } + b ^{ 3 } + c ^{ 3 } − 3abc = (a + b + c) (a ^{ 2 } + b ^{ 2 } + c ^{ 2 } − ab − bc − ac)
a ^{ 3 } + b3 + c ^{ 3 } − 3abc = (0) (a ^{ 2 } + b ^{ 2 } + c ^{ 2 } − ab − bc − ac)
a ^{ 3 } + b ^{ 3 } + c ^{ 3 } − 3abc = 0
a ^{ 3 } + b ^{ 3 } + c ^{ 3 } = 3abc
Check Algebra Formulas for full list of formulas
Next: Ex 2.4, 9 (i) → Go Adfree
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Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.