To simplify the expression, let's break it down step by step:

1. Start with the expression (căn 7 - căn 3)(căn 3 + căn 7) - 1.

2. Simplify the first part, căn 7 - căn 3:
- căn 7 is an irrational number, so it cannot be simplified further.
- căn 3 is also an irrational number, so it cannot be simplified further.
- Therefore, căn 7 - căn 3 cannot be simplified any further.

3. Simplify the second part, căn 3 + căn 7:
- căn 3 is an irrational number, so it cannot be simplified further.
- căn 7 is also an irrational number, so it cannot be simplified further.
- Therefore, căn 3 + căn 7 cannot be simplified any further.

4. Multiply the simplified parts together:
- (căn 7 - căn 3)(căn 3 + căn 7) = (căn 7)(căn 3) + (căn 7)(căn 7) - (căn 3)(căn 3) - (căn 3)(căn 7)
- Since căn 7 and căn 3 are both irrational numbers, their product cannot be simplified further.
- Therefore, (căn 7 - căn 3)(căn 3 + căn 7) cannot be simplified any further.

5. Subtract 1 from the result:
- (căn 7 - căn 3)(căn 3 + căn 7) - 1 = (căn 7)(căn 3) + (căn 7)(căn 7) - (căn 3)(căn 3) - (căn 3)(căn 7) - 1
- Since the expression cannot be simplified any further, we leave it as is.

Therefore, the simplified form of the expression (căn 7 - căn 3)(căn 3 + căn 7) - 1 is (căn 7)(căn 3) + (căn 7)(căn 7) - (căn 3)(căn 3) - (căn 3)(căn 7) - 1.