Answer
$(2x)(x+6+2a)(x+6-2a)$
Work Step by Step
$2x^{3}-8a^{2}x+24x^{2}+72x$
Rearrange the terms to match the proper order.
$=2x^{3}+24x^{2}+72x-8a^{2}x$
Factor out the common factor $2x$ from the expression.
$=2x(x^{2}+12x+36-4a^{2})$
Group the first three terms. This is the perfect square trinomial.
$=2x((x^{2}+12x+36)-4a^{2})$
The formula for it can be used here is
$ A^{2}+ 2.A.B+B^{2} =(A+B)^{2}$
Using the formula, factor the perfect square trinomial.
$[x^{2}+2.x.6+6^{2}= (x+6) ^{2}$
$x^{2}+12x+36= (x+6) ^{2}]$
$=2x((x+6) ^{2}-4a^{2})$
$=2x((x+6) ^{2}-(2a)^{2})$
Factor the difference of squares. The factors are the sum and difference of the expressions being squared.
Using the formula $[(a^{2}-b^{2}) = (a+b)(a-b)]$
$=(2x)(x+6+2a)(x+6-2a)$
