It is possible (and allowed) to take the expenses for a credit and have the student claim the scholarship as income.
The credit is usually worth more that the tax on the scholarships.
If the student is your dependent, you get the credit and the student claims the taxable scholarship as income.
The student may or may not need to file depending on the amount of the taxable scholarship and any other income the student has.
For more information please look at IRS Pub 970.
IRS Pub 970
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