You can't "double dip" and use the same expenses for a credit and then also allocated to a distribution.
It might, or might not matter.
Box 1 of a 1098-T reports Tuition. Box 5 reports Scholarships.
Subtract Box 5 from Box 1, what is the "remaining expense"?
NOW subtract the distribution from this "remaining expense", what is left?
If you are getting the American Opportunity Tax Credit, that credit "Maxes Out" with 4,000 expense.
If you are still left with 4,000 expenses after subtracting scholarships and distributions from Tuition, you get the full American Opportunity Tax Credit and the student needn't claim any of the distribution.
If the expenses are LESS THAN 4,000, remember to add books, supplies and in your case up to 3,220 Room and Board Expense since a distribution can USUALLY be used to pay Room and Board.
The main issue is that an expense cannot be used for a credit and also to offset tax-free assistance, such as a scholarship, or distribution.
IRS PUB 970 does a good job explaining-
Pub 970
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