Identities V

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