a+b+c=a²+b²+c²+2ab+2bc+2ca prove it please
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The formula is:
a2+b2+c2+2ab+2bc+2ca
PROOF:-
(a+b+c)2 can be written as (a+b+c)*(a+b+c),
Therefore, (a+b+c)2=(a+b+c)∗(a+b+c)(a+b+c)2=(a+b+c)∗(a+b+c)
=a(a+b+c)+b(a+b+c)+c(a+b+c)=a(a+b+c)+b(a+b+c)+c(a+b+c)
=a2+ab+ca+ab+b2+bc+ca+bc+c2=a2+ab+ca+ab+b2+bc+ca+bc+c2
=a2+b2+c2+ab+ab+bc+bc+ca+ca=a2+b2+c2+ab+ab+bc+bc+ca+ca
=a2+b2+c2+2ab+2bc+2ca
a2+b2+c2+2ab+2bc+2ca
PROOF:-
(a+b+c)2 can be written as (a+b+c)*(a+b+c),
Therefore, (a+b+c)2=(a+b+c)∗(a+b+c)(a+b+c)2=(a+b+c)∗(a+b+c)
=a(a+b+c)+b(a+b+c)+c(a+b+c)=a(a+b+c)+b(a+b+c)+c(a+b+c)
=a2+ab+ca+ab+b2+bc+ca+bc+c2=a2+ab+ca+ab+b2+bc+ca+bc+c2
=a2+b2+c2+ab+ab+bc+bc+ca+ca=a2+b2+c2+ab+ab+bc+bc+ca+ca
=a2+b2+c2+2ab+2bc+2ca
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