#### Answer

$(2b+7)(5a-3)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
10ab-21-6b+35a
,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and fourth terms and the second and third terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(10ab+35a)-(21+6b)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5a(2b+7)-3(7+2b)
\\\\=
5a(2b+7)-3(2b+7)
.\end{array}
Factoring the $GCF=
(2b+7)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2b+7)(5a-3)
.\end{array}