Education

The dependent student received 55,447 in scholarships. 

Tuition paid to the school was 27, 489

We don't know about books and supplies

We don't know about Room and Board

We don't know the amount on the 1099-Q

There can be income tax on a 1099-Q distribution and also a penalty tax if a distribution is made and not used for education expenses. Both the account owner and the beneficiary can make distributions. The person that makes the distribution is listed on the 1099-Q and they are liable for the tax (if any).

The penalty tax on a distribution is waved if the student earned a scholarship for as much or more than the distribution. 

The income tax is waived if the distribution was used for education expenses. 

Education expenses that can offset a 1099-Q include the same expenses that an education credit is based on (Tuition, Fees, Books, Supplies) AND expenses that don't qualify for a credit, Room and Board. 

If the distribution is taxed, the tax is calculated on a ratio of earnings to basis (contributions) so there is a bit of a calculation.

Numbers and expenses can be moved around (within reason) to obtain an education credit. 

Yes, you have the option to have the student pay tax on scholarship money in order to "free-up" expenses for the credit, and if there were no 1099-Q, your numbers would be correct, the student could claim 31,958 which gives you 4,000 education expenses to use for the credit. 

Variables include 

What will be the tax bill for the student?

Are you eligible for the credit (your income level) ?

How much was the 1099-Q distribution and what was it used for?

Did the student have expenses not listed on the 1098-T such as books and supplies?

The American Opportunity Tax Credit is only good four times, will the student have more expenses in the next four years (as an undergrad) so you should "save" the credit for those years? 

If the distribution was used for Room and Board and the Room and Board expense was as much or more than the distribution, the distribution won't be a factor and the room and board will also not be a factor. 

This is because only the distribution can go against Room and Board, Room and Board can't go towards a credit. 

If the room and board zeros out the distribution, the distribution is of no consequence and any remaining room and board expense is useless. 

If the distribution was more than room and board, the person that was issued the 1099-Q will need to claim some of that as income OR some education expense will need to be allocated to the distribution. 

IRS Pub 970 has lots of good information.