<p>No they are not mutually exclusive. </p>
<p>Line 31 on the 1040a is for the nonrefundable part of the credit - the part that reduces the tax liability. (it is also where other education credits such as the lifetime learning - which is all non refundable would appear).</p>
<p>Line 43 is the refundable part of the AO credit.</p>
<p>Someone with a tax liability that was eligible for the non refundable part of the credit would have an amount in line 31 and also an amount in line 43. </p>
<p>The majority of tax credits are non refundable and therefore only reduce a persons tax liability. Therefore most tax credits will appear on the tax return after the tax line (28 - which is where your tax liability based on your taxable income is reported) and before the total tax line (line 37).</p>
<p>Refundable tax credits appear after the total tax line because you can get them even when you have no tax liability. The tax return effectively treats the refundable tax credits as if you had actually already paid this amount in taxes and they are therefore being refunded to you.</p>