1. **State the problem:** Calculate the value of $193^2 - 7^2$. 2. **Use the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ where $a = 193$ and $b = 7$. 3. **Apply the formula:** $$193^2 - 7^2 = (193 - 7)(193 + 7)$$ 4. **Calculate each term:** $$193 - 7 = 186$$ $$193 + 7 = 200$$ 5. **Multiply the results:** $$186 \times 200 = 37200$$ 6. **Final answer:** $$193^2 - 7^2 = 37200$$