#### Answer

$a(ab-7c)(ab+7c)$

#### Work Step by Step

RECALL:
A difference of two squares can be factored using the formula:
$x^2-y^2=(x-y)(x+y)$
Factor out the greatest common factor, $a$, to obtain:
$=a(a^2b^2-49c^2)
\\=a[(ab)^2-(7c)^2]$
The binomial is a difference of two squares.
Factor the given difference of two squares using the formula above with $x=ab$ and $b=7c$ to obtain:
$=a(ab-7c)(ab+7c)$