Okay, let's tackle this math problem step by step. The question is asking for the value of (26² - 24² - 10)² - 10². Hmm, that looks a bit complicated, but maybe I can break it down.

First, I need to compute the inner part: 26 squared minus 24 squared minus 10. Then, take that result and square it, and finally subtract 10 squared. Let me start with the exponents.

Calculating 26 squared: 26 times 26. Let me do that. 25 squared is 625, so 26 squared is 25² + 2*25 + 1 = 625 + 50 + 1 = 676. Wait, no, that's for (25 + 1)². Alternatively, 26*26. Let me multiply it out: 20*20 = 400, 20*6 = 120, 6*20 = 120, 6*6=36. So 400 + 120 + 120 + 36 = 676. Yeah, that's right.

Then 24 squared. 24*24. Let's do that. 20*20=400, 20*4=80, 4*20=80, 4*4=16. So 400 + 80 + 80 +16= 576. So 24 squared is 576. Okay.

So substituting back into the inner part: 26² -24² -10 = 676 -576 -10. Let's compute that. 676 -576 is 100, right? Then 100 -10 is 90. So the inner part is 90.

Now, the next step is to square that result. So 90 squared. Let me calculate that. 90*90. Well, 9*9=81, and since there are two zeros, it's 8100. So 90² is 8100.

Then, subtract 10 squared. 10 squared is 100. So 8100 -100. That's straightforward. 8100 minus 100 is 8000. So the final result should be 8000.

Wait, let me double-check each step to make sure I didn't make any mistakes. 

First, 26²: 26*26. Let me verify once again. 25² is 625, so 26² is 25² + 2*25 +1 = 625 +50 +1=676. Correct. 

24²: 24*24. 20*20=400, 20*4=80, 4*20=80, 4*4=16. 400+80+80+16=576. Correct.

676 -576 = 100. Then 100 -10=90. So the inner part is 90. Then 90²=8100. Then subtract 10²=100. 8100-100=8000. All steps check out. 

Alternatively, maybe there's a smarter way to compute the original expression. Let me see. The expression is (26² -24² -10)² -10². Notice that 26² -24² is a difference of squares. The difference of squares formula is a² - b² = (a - b)(a + b). So applying that here, 26² -24² = (26 -24)(26 +24) = (2)(50) = 100. Then subtract 10: 100 -10 =90. Then square and subtract 10², which gives 8000. Same result. So that's a quicker way. 

Either method, the answer is 8000. So I think that's correct. Let me just confirm once more. 

Yes, 26² is 676, 24² is 576. 676 -576 is 100. 100 -10 is 90. 90 squared is 8100. 8100 -100 is 8000. Yep, that's right. 

I don't see any mistakes here. The key was recognizing that 26² -24² is a difference of squares, which simplifies the calculation. Then subtract 10, square the result, and subtract another 10². All steps lead to 8000. So the final answer should be 8000.
Therefore, the value of $(26^2 - 24^2 - 10)^2 - 10^2$ is $\boxed{8000}$.
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