$\displaystyle \left(\sqrt{x+2}+2\right)^2=\left(\sqrt{x+2}+2\rig ht)\left(\sqrt{x+2}+2\right)$
$\displaystyle =\left(\sqrt{x+2}\right)\left(\sqrt{x+2}\right)+\l eft(\sqrt{x+2}\right)2+2\left(\sqrt{x+2}\right)+2( 2)$
just as
$\displaystyle 5^2=25$
$\displaystyle (3+2)^2=(3+2)(3+2)=3(3+2)+2(3+2)=3(3)+3(2)+2(3)+2( 2)$
$\displaystyle =9+6+6+4=25$