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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