#### Answer

$7g^3h^2 \left( 3g^4-g^2h^2+20h^4 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Get the $GCF$ of the given expression, $
21g^7h^2-7g^5h^4+140g^3h^6
.$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
21,-7,140
\}$ is $
7
$ since it is the highest number that can evenly divide (no remainder) all the given constants.
The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
g^7h^2,g^5h^4,g^3h^6
\}$ is $
g^3h^2
.$
Hence, the entire expression has $GCF=
7g^3h^2
.$
Factoring the $GCF=
7g^3h^2
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
7g^3h^2 \left( \dfrac{21g^7h^2}{7g^3h^2}-\dfrac{7g^5h^4}{7g^3h^2}+\dfrac{140g^3h^6}{7g^3h^2}
\right)
\\\\=
7g^3h^2 \left( 3g^4-g^2h^2+20h^4 \right)
.\end{array}