Answer
$6(x + 5)^3(x - 1)(x+1)$
Work Step by Step
We factor out $(x + 5)^3(x - 1)$ and distribute, combine like terms, and simplify as follows:
\begin{align*}
4(x + 5)^3(x - 1)^2 &+ (x + 5)^4 \cdot2(x - 1)\\
&=(x + 5)^3(x - 1)[4(x-1)+2(x+5)]\\
&=(x + 5)^3(x - 1)[4x-4+2x+10]\\
&=(x + 5)^3(x - 1)(6x+6)\\
&=6(x + 5)^3(x - 1)(x+1).
\end{align*}
