Final answer:
The number of unique permutations of the word ALGEBRA is 2520.
Step-by-step explanation:
The number of unique permutations of the word ALGEBRA can be found using the formula for permutations of a word with repeated letters. The word ALGEBRA has 7 letters, out of which A appears twice and B appears twice. So, the number of unique permutations is given by 7!/2!2!. This simplifies to 7x6x5x4x3x2x1/2x1x2x1, which equals 2520. Therefore, there are 2520 unique permutations of the word ALGEBRA.