Question 183921
Factor completely: Note: You can indicate exponents by use of the caret symbol (^).  Example - a-squared would look like a^2
{{{-36a^2b+21ab^2-3b^3}}} First factor out those factors that are common to each term, in this case, I would factor out -3b thus:
{{{-3b(12a^2-7ab+b^2)}}} Notice the change of sign on each factor when you factor the -3.
Now to factor the trinomial in parentheses, first look at the leading term, ({{{12a^2}}}), and note that this can be factored as:
{{{12a^2 = 1*12*a*a}}} or {{{-1*-12*a*a}}}
{{{12a^2 = 2*6*a*a}}} or {{{-2*-6*a*a}}}
{{{12a^2 = 3*4*a*a}}} or {{{highlight(-3*-4*a*a)}}}
Now notice the middle term, {{{-7ab}}} The only way to factor this is:
{{{-7ab = -7*a*b}}} and you can get {{{-7}}} by adding {{{highlight(-3+(-4))}}} and the last term {{{b^2}}} can only be factored as {{{highlight(b*b)}}}
So putting it all together, you get:
{{{-36a^2b+21ab^2-3b^3 = highlight(-3b(3a-b)(4a-b))}}}