\(\left(a+4\right)^2-16a^2\)
\(=\left(a+4\right)^2-\left(4a\right)^2\)
\(=\left(a+4+4a\right)\left(a+4-4a\right)\)
\(=\left(5a+4\right)\left(4-3a\right)\)
\(x^3=4x\)
\(\Leftrightarrow x^3-4x=0\)
\(\Leftrightarrow x\left(x^2-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^2-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm\sqrt{4}=\pm2\end{cases}}\)