Identity VII is

  • a 3 + b 3 + c − 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

  1. Chapter 2 Class 9 Polynomials
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.