Answer
$16 a b^2 \sqrt{7 a b}+4 b \sqrt{7 a}$
Work Step by Step
Given \begin{equation}
2 a \sqrt{7 a b^5}+7 b \sqrt{28 a^3 b^3}+4 b \sqrt{7 a}.
\end{equation} Simplify each of the first two terms and collect like terms.
\begin{equation}
\begin{aligned}
2 a \sqrt{7 a b^5}&=2 a \sqrt{7a b^4\cdot b}\\
&= 2ab^2 \sqrt{7ab} \\
7 b \sqrt{28 a^3 b^3}& = 7 b \sqrt{4\cdot 7 a^2\cdot a b^2\cdot b}\\
&= 7b(2ab) \sqrt{7ab}\\
&= 14ab^2 \sqrt{7ab}.
\end{aligned}
\end{equation} Now, add the the like terms to get the final simplified expression.
\begin{equation}
\begin{aligned}
& 2 a \sqrt{7 a b^5}+7 b \sqrt{28 a^3 b^3}+4 b \sqrt{7 a}=2ab^2 \sqrt{7ab}+ 14ab^2 \sqrt{7ab} +4 b \sqrt{7 a}\\
& =16 a b^2 \sqrt{7 a b}+4 b \sqrt{7 a}.
\end{aligned}
\end{equation} The solution is
\begin{equation}
2 a \sqrt{7 a b^5}+7 b \sqrt{28 a^3 b^3}+4 b \sqrt{7 a}=16 a b^2 \sqrt{7 a b}+4 b \sqrt{7 a}.
\end{equation}
