#### Answer

$x+5+ 4(\sqrt (x+1)$

#### Work Step by Step

Step 1: We will use the expression $(a+b)^{2}=a^{2}+2ab + b^{2}$
Step 2: $a=\sqrt (x+1)$ and $b=2$
Step 3: Substituting $a$ and $b$ in the above expression,
$(\sqrt (x+1) +2)^{2}$ = $(\sqrt (x+1))^{2} +2(\sqrt (x+1))(2) + 2^{2}$
Step 4: Simplifying, $(x+1) + 2(2)(\sqrt (x+1) + 4$= $(x+1) + 4(\sqrt (x+1) + 4$
Step 5: Simplifying further, $x+1+4+ 4(\sqrt (x+1)$
Step 6: $x+5+ 4(\sqrt (x+1)$