Answer
$2x(x+7-7a)(x+7+7a)$
Work Step by Step
$ 2x^{3}-98a^{2}x+28x^{2}+98x=\quad$...... we have a common factor, $2x$
$=2x(x^{2}-49a^{2}+14x+49)$
... the terms not containing $a$ form a recognizable trinomial
$=2x[(x^{2}+14x+49)-49a^{2}]$
$=2x[(x^{2}+2\cdot 7x+7^{2})-49a^{2}]$
... a square of a sum, $A^{2}+2AB+B^{2}=(A+B)^{2}$
$=2x[(x+7)^{2}-49a^{2}]$
... the brackets contain a difference of squares, $(x+7)^{2}-(7a)^{2}$
=$2x(x+7-7a)(x+7+7a)$
