a2+b2+c2 is equal to ?
Let us multiply a+b+c by itself, we get;
(a+b+c)(a+b+c)=a2+ab+ac+ba+b2+bc+ca+cb+c2 (after multiplying the brackets)
We know that ab=ba,ac=ca,bc=cb and put these values we get
(a+b+c)(a+b+c)=a2+ab+ac+ab+b2+bc+ac+bc+c2=a2+b2+c2+2ab+2bc+2ac
Now we get (a+b+c)2=a2+b2+c2+2ab+2bc+2ca
Hence a2+b2+c2is equal to (a+b+c)2-2ab-2bc-2ca