Answer
The expression can be expressed in simplest form as ${{\left( 2x+1 \right)}^{3}}=8{{x}^{3}}+12{{x}^{2}}+6x+1$
Work Step by Step
Thus, we get
$\begin{align}
& {{\left( 2x+1 \right)}^{3}}=\left( \begin{matrix}
3 \\
0 \\
\end{matrix} \right){{\left( 2x \right)}^{3}}+\left( \begin{matrix}
3 \\
1 \\
\end{matrix} \right){{\left( 2x \right)}^{2}}\cdot 1+\left( \begin{matrix}
3 \\
2 \\
\end{matrix} \right)\left( 2x \right){{\left( 1 \right)}^{2}}+\left( \begin{matrix}
3 \\
3 \\
\end{matrix} \right){{\left( 1 \right)}^{3}} \\
& =\frac{3!}{0!\left( 3-0 \right)!}\left( 8{{x}^{3}} \right)+\frac{3!}{1!\left( 3-1 \right)!}\left( 4{{x}^{2}} \right)+\frac{3!}{2!\left( 3-2 \right)!}\left( 2x \right)+\frac{3!}{3!\left( 3-3 \right)!} \\
& =8{{x}^{3}}+3\left( 4{{x}^{2}} \right)+3\left( 2x \right)+1 \\
& =8{{x}^{3}}+12{{x}^{2}}+6x+1
\end{align}$
