Question 7131
Well, you could start by factoring a 2 from the expression, just to simplify it a bit.

{{{2a^2 - 2ab - 24b^2}}} = {{{2(a^2 - ab - 12b^2)}}}
Now let's look at the expression in the parentheses: {{{a^2 - ab - 12b^2}}}
The factors of the first term , {{{a^2}}} would be {{{(a)(a)}}}
Look at the last term: {{{-12b^2}}} and ask what are the factors of this term?

{{{-12b^2}}} = {{{(3b)(-4b)}}} or {{{(-3b)(4b)}}} just to name a couple.

So, now try: {{{(a + 3b)(a - 4b)}}} Using the FOIL method, multiply these factors:

{{{(a + 3b)(a - 4b) = (a^2 - 4ab + 3ab - 12b^2)}}} Simplify to get:
{{{a^2 - ab - 12b^2}}} and if you multiply by the 2 we factored at the start, we'll get:

{{{2a^2 - 2ab - 24b^2}}}

So, the factors are: {{{2(a+3b)(a-4b)}}}