Question

Factor the expression completely 81m + 48mn

Answer 1

To factor the expression \( 81m + 48mn \) completely, we first look for the greatest common factor (GCF) of the terms.

1. Identify the GCF of the coefficients:
- The coefficients are 81 and 48. The GCF of 81 and 48 is 3.

2. Identify the common variable:
- Both terms have the variable \( m \) in common.

3. Combine the GCF from the coefficients and the common variable:
- The GCF is \( 3m \).

4. Factor \( 3m \) out of the expression:
\[
81m + 48mn = 3m(27 + 16n)
\]

So, the expression \( 81m + 48mn \) factored completely is:
\[
\boxed{3m(27 + 16n)}
\]