If $x,y,z.\geq 0$ and $x+y+z = 10$ , Then Max. value of $xyz+xy+yz +zx$, If $x,y,z.\geq 0$ and $x+y+z = 10$ , Then Maximum value of $xyz+xy+yz +zx$, is
$\bf{My\; Try::}$ First we can write the given expression
$xyz+xy+yz+zx = (x+1)(y+1)(z+1)-(x+y+z)-1 = $
$\displaystyle = (x+1)(y+1)(z+1)-\left\{(x+1)+(y+1)+(z+1)\right\}+2$. 
So we can write $x+y+z = 10$ as $(x+1)+(y+1)+(z+1) = 13$ 
Now Let $\displaystyle (x+1)=a\geq 1\;\;,(y+1)=b\geq 1$ and $(z+1)=c\geq 1$
So expression convert into $a+b+c=13\;\;,a,b,c\geq 1$ and Maximize $abc-(a+b+c)+2$
Now How can i solve after that, Help me
Thanks 

Use the fact that $a+b+c=13$ to say you are trying to maximize $abc-14$, which is the same as maximizing $abc$.  The AM-GM inequality now tells you that $a=b=c$
