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Factor the expression completely 81m + 48mn

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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: \[ \boxed{3m(27 + 16n)} \]