3x3y + 12xy − 9x2y − 36y rewrite the expression completely factored. show the steps of your work.

3y(x²+4)(x-3)

First we factor out the GCF.  All of the terms are divisible by 3 and all have a y, so the GCF is 3y:

3y(x³+4x-3x²-12)

Now we group the polynomial (first two together, last two together):
3y[(x³+4x)+(-3x²-12)]

The GCF of the first group is x; the GCF of the second group is -3.  We factor these out:
3y[x(x²+4)-3(x²+4)]

Factoring out the GCF of the two groups,
3y(x²+4)(x-3)