To solve the expression \(987654321^2 - 987654320 \times 987654322\), let's break it down step by step.

1. First, compute \(987654321^2\):
   \[
   987654321^2 = 987654321 \times 987654321 = 975461057789971041
   \]

2. Next, compute \(987654320 \times 987654322\):
   \[
   987654320 \times 987654322 = 975461057789971040
   \]

3. Now, subtract the two results:
   \[
   987654321^2 - 987654320 \times 987654322 = 975461057789971041 - 975461057789971040 = 1
   \]

So, the final result is \( \boxed{1} \).

Would you like further details or have any questions? Here are some related questions:

1. What is the general formula for the difference of squares?
2. How do you simplify large exponentiations without a calculator?
3. Can this expression be solved using algebraic identities?
4. How would the solution change if the numbers were slightly different?
5. How does this problem relate to the properties of multiplication and subtraction?

**Tip:** When dealing with large numbers, look for patterns or algebraic identities that can simplify the calculations.

Learn how to solve the expression 987654321 squared minus 987654320 times 987654322 step-by-step with detailed calculations and explanations. Explore the concepts of large number arithmetic, exponentiation, and multiplication. Suitable for advanced mathematics enthusiasts and learners.

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