2bx - 3ay - 6by + ax

To simplify the expression \(2bx - 3ay - 6by + ax\), we can group the like terms:

1. Rearranging the expression gives: \[ ax + 2bx - 3ay - 6by \]

2. Grouping the like terms: \[ (ax + 2bx) + (-3ay - 6by) \]

3. Factor out common factors from each group:

   • From \(ax + 2bx\), factor out \(x\): \[ x(a + 2b) \]
   • From \(-3ay - 6by\), factor out \(-3y\): \[ -3y(a + 2b) \]

4. Now the expression can be rewritten as: \[ x(a + 2b) - 3y(a + 2b) \]

5. Finally, factor out the common factor \((a + 2b)\): \[ (a + 2b)(x - 3y) \]

Thus, the simplified form of the expression \(2bx - 3ay - 6by + ax\) is: \[ (a + 2b)(x - 3y) \]