Answer
$2a^3(5a+1)(2a+5)$
Work Step by Step
Factoring the $GCF=2a^3$ results to $
2a^3(10a^2+27a+5)
$. The 2 numbers whose product is $ac=
10(5)=50
$ and whose sum is $b=
27
$ are $\left\{
2, 25
\right\}$. Using these numbers to decompose the middle term results to
\begin{array}{l}
2a^3(10a^2+2a+25a+5)
\\\\=
2a^3[(10a^2+2a)+(25a+5)]
\\\\=
2a^3[2a(5a+1)+5(5a+1)]
\\\\=
2a^3[(5a+1)(2a+5)]
\\\\=
2a^3(5a+1)(2a+5)
.\end{array}
