12 а^2в^4-36а^2в+44авс=

To factor the expression \( 12a^2b^4 - 36a^2b + 44abc \), we can start by identifying common factors in each term.

1. First, let's look for the common factors:

   • The coefficients are \(12\), \(-36\), and \(44\). The greatest common factor (GCF) of these numbers is \(4\).
   • For the variables, we have \(a^2\) in the first two terms and \(ab\) in the third term. The common factor here is \(ab\).

2. Now, let's factor out \(4ab\): \[ 12a^2b^4 - 36a^2b + 44abc = 4ab(3ab^3 - 9a + 11c) \]

3. Now we will check if \(3ab^3 - 9a + 11c\) can be factored further:

   • The first term \(3ab^3\) cannot be factored with the others easily, and \( -9a \) and \(11c\) do not share any common terms either.

Thus, the final factored form of the expression is: \[ 4ab(3ab^3 - 9a + 11c) \]