Factor completely. Be sure to factor out the greatest common factor first if it is other than 1. (If the polynomial is prime, enter PRIME.)

56a^2+39ab-27b^2

Can't really factor anything out of this.

(7 a - 3 b) (8 a + 9 b)

If you FOIL:

you get 56a^2+39ab-7b^2

I just kind of did trial and error.

To factor the given polynomial, we first need to check if there is a greatest common factor (GCF) that can be factored out. In this case, the GCF of the polynomial is 1 since there are no common factors other than 1.

Now, let's factor the polynomial: 56a^2 + 39ab - 27b^2

To factor a trinomial like this, we look for two binomials in the form:
(ax + by) (cx + dy), where a, b, c, and d represent coefficients.

In order to find the values of a, b, c, and d, we can consider the coefficient of each term in the given polynomial.

For the first term, 56a^2, the only possible factors are 1, 2, 4, 7, 8, 14, 28, and 56.

For the last term, -27b^2, the possible factors are 1, 3, 9, 27.

Now, we need to find combinations of these factors that satisfy the middle term, 39ab.

After trying different combinations, we find that 8 and 7 work. So the factors are likely to have a coefficient of 8 and 7 respectively.

Therefore, we can write the factored form as:
(8a - 9b)(7a + 3b)

So, the completely factored form of the given polynomial is:
(8a - 9b)(7a + 3b)