\( 89 m - 109 n - 12 b m + 15 b n \)

To simplify and factor the expression: \[ 89m - 109n - 12bm + 15bn \] **Step 1: Group Like Terms** Group the terms involving \( m \) and the terms involving \( n \): \[ (89m - 12bm) + (-109n + 15bn) \] **Step 2: Factor Out Common Variables** - From the first group \( (89m - 12bm) \), factor out \( m \): \[ m(89 - 12b) \] - From the second group \( (-109n + 15bn) \), factor out \( n \): \[ n(-109 + 15b) \] **Step 3: Rewrite the Expression** Combine the factored terms: \[ m(89 - 12b) + n(-109 + 15b) \] Alternatively, you can write it as: \[ m(89 - 12b) - n(109 - 15b) \] **Final Factored Form:** \[ 89m - 109n - 12bm + 15bn = m(89 - 12b) + n(-109 + 15b) \] or \[ m(89 - 12b) - n(109 - 15b) \] This is the simplified and factored form of the given expression.