Identity V is

(a + b + c) 2 = a 2 + b 2 + c 2  + 2ab + 2bc + 2ca

 

Let us prove it

Proof :

(a + b + c) 2

= ((a + b) + c) 2

Using (x + y) 2 = x 2 + y 2 + 2xy

= (a + b) 2 + c 2 + 2(a + b)c

= (a + b) 2 + c 2 + 2ac + 2bc

Using (x + y) 2 = x 2 + y 2 + 2xy

= a 2 + b 2 + 2ab + c 2 + 2ac + 2bc

= a 2 + b 2 + c 2 + 2ab + 2ac + 2bc

 

 Check more algebra formulas .

 

 

Lets take an example

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

(2 + 3 + 4)2 = 22 + 32 + 42 + 2(2)(3) + 2(3)(4) + 2(4)(2)

(9)2 = 4 + 9 + 16 + 12 + 24 + 16

81 = 4 + 9 + 16 + 12 + 24 + 16

81 = 81

  1. Chapter 2 Class 9 Polynomials
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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.