Identities V

Last updated at Dec. 16, 2024 by

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

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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 and Computer Science at Teachoo