Answer
The graphs are not the same.
Work Step by Step
Given
\begin{equation}
\begin{aligned}
& (\sqrt{x}+2)(\sqrt{x}-2)=x^2-4 \\
& {[0,10,1] \text { by }[-10,10,1]}
\end{aligned}
\end{equation}
Let
\begin{equation}
\begin{aligned}
f(x)&= (\sqrt{x}+2)(\sqrt{x}-2) \\
g(x)&=x^2-4 \\
\end{aligned}
\end{equation}
The graphs of both functions are shown in the figure and are clearly not the same. They will be identical if we choose:
\begin{equation}
\begin{aligned}
g(x)&= (\sqrt{x}+2)(\sqrt{x}-2)\\
&=x-4 \\
\end{aligned}
\end{equation}
