The "Adjusted Qualified Education Expenses" are reduced by the "Tax-Free" assistance.
If the 25,000 includes room and board, yes, it would be reduced to 15,000. If the 25,000 is tuition and fees only, the scholarship can be applied to room and board instead, leaving 25,000 for the early withdrawal.
You can even apply the scholarship to the tuition (making the scholarship tax-free) and use room and board to avoid the IRA penalty.
According to the IRS:
“Qualified education expenses. For purposes of the
10% additional tax, these expenses are tuition, fees, books, supplies, and
equipment required for enrollment or attendance at an eligible educational
institution. They also include expenses for special needs services incurred by
or for special needs students in connection with their enrollment or
attendance.
In addition, if the student is at least a half-time student,
room and board are qualified education expenses.”
https://www.irs.gov/pub/irs-pdf/p970.pdf
