12 а^2в^4-36а^2в+44авс=

To simplify the expression \( 12a^2b^4 - 36a^2b + 44abc \), we can start by factoring out the greatest common factor (GCF) from all the terms.

1. Identify the GCF of the coefficients: The GCF of \( 12, -36, \) and \( 44 \) is \( 4 \).
2. Identify the GCF of the variable parts: Each term has at least one \( a \) and one \( b \). Therefore, the GCF for the variable parts is \( 4ab \).

Now, factor \( 4ab \) out of the expression:

\[ 12a^2b^4 - 36a^2b + 44abc = 4ab(3ab^3 - 9a + 11c) \]

So, the simplified expression is:

\[ 4ab(3ab^3 - 9a + 11c) \]

This is the factored form of the original expression.