Beginning Algebra With Applications, Chapter 8, 8.2, Section 8.2, Problem 72

Factor $2a^3 + 6a^2 + 4a$


$
\begin{equation}
\begin{aligned}

2a^3 + 6a^2 + 4a =& 2a(a^2 + 3a + 2)
&& \text{Factor out } 2a
\\
=& 2a(a+1)(a+2)
&& \text{Factor } a^2 + 3a + 2

\end{aligned}
\end{equation}
$