You should report the alimony you paid on your return, along with your ex-spouse's social security number.
For information on what the requirements are for "deductible" alimony payments click here
How much of a difference will it make for you? It depends on what your tax rate is. Go to the link below and look at the tax brackets by filing status. The approximate difference would be the amount of alimony multiplied by the applicable tax rates. However, if you have tax credits that could change the calculation.