<s>[INST] Expand $(a−b)^2 +(b−c)^2 +(a−c)^2$ , and hence prove that $a ^2 +b^2 +c^2 ≥ ab+bc+ac$. I would like some advice on how I can prove that  $$a^2 +b^2 +c^2 ≥ ab+bc+ac.$$
I have completed the first part of the question that asks for an expansion:
$$ (a−b)^2 +(b−c)^2 +(a−c)^2$$
$$(a^2-2ab+b^2)+(b^2-2bc+c^2)+(a^2-2ac+c^2)$$
$$ 2a^2+2b^2+2c^2-2ab-2bc-2ac $$
$$ 2(a^2+b^2+c^2-ab-bc-ac)$$
If I have done the expansion incorrectly, corrections in this aspect would also be helpful. 
 [/INST] Hint: $(a-b)^2 + (b-c)^2 + (c-a)^2 \geq .....0$
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