problem: What is the value of $(26^2 - 24^2 - 10)^2 - 10^2$?
solution: We know that $x^2 - y^2 = (x+y)(x-y)$. To begin with, let $x = 26^2 - 24^2 - 10$ and $y = 10$. Factoring $x^2 - y^2$ and substituting in gives $(26^2-24^2-10+10)(26^2-24^2-10-10)$. Now, let $x = 26$ and $y = 24$. Factoring $x^2 - y^2$ and substituting in gives $((26+24)(26-24)-10+10)((26+24)(26-24)-10-10)$. This simplifies to $(50\cdot 2)(50 \cdot 2 - 20)$, or $100 \cdot 80$. Thus, our final answer is $\boxed{8000}$.