Proving that for reals $a,b,c$,  $(a + b + c)^2 \leq 3(a^2+b^2+c^2)$ 
Proving that for reals $a,b,c$, $(a+b+c)^2\leq 3(a^2+b^2+c^2)$.

This is a homework question and I have no clue where to even start on this. I don't know if I am just tired or what but I can't get anywhere. I've expanding both sides and seeing if that gets me anywhere but I don't see how it helps.

We need to expand both sides of inequality:
$(a+b)^2+c^2+2(a+b)c\leq 3a^2+3b^2+3c^2$
$a^2+b^2+c^2+2ab+2ac+2bc\leq 3a^2+3b^2+3c^2$
$2ab+2ac+2bc\leq 2a^2+2b^2+2c^2$
$0\leq a^2+b^2-2ab+a^2+c^2-2ac+b^2+c^2-2bc$
$0\leq (a-b)^2 +(a-c)^2
+(b-c)^2$  , what is obvious true.
