I need to compute 987654321² exactly.

Let me use the algebraic approach by recognizing that 987654321 = 10⁹ - 111111111.

First, let me verify what 111111111 is:
111111111 = (10⁹ - 1)/9

So 987654321 = 10⁹ - (10⁹ - 1)/9 = (9·10⁹ - 10⁹ + 1)/9 = (8·10⁹ + 1)/9

Actually, let me use a more direct approach. I'll recognize that:
987654321 = 10⁹ - 12345679

Wait, let me be more systematic. Let me compute this directly:
987654321 = 1000000000 - 12345679

So:
987654321² = (1000000000 - 12345679)²
= 1000000000² - 2(1000000000)(12345679) + 12345679²

Let me calculate each part:
- 1000000000² = 10¹⁸ = 1000000000000000000
- 2(1000000000)(12345679) = 24691358000000000
- 12345679² = ?

For 12345679²:
12345679² = (1.2345679 × 10⁷)²

Let me compute this step by step:
12345679² 

I'll use the fact that 12345679 × 9 = 111111111, so 12345679 = 111111111/9.

Therefore: 12345679² = (111111111/9)² = 111111111²/81

Now, 111111111² can be computed as:
111111111² = (10⁹ - 1)²/9² × 9² = (10⁹ - 1)²/9²  × 9² = (10⁹ - 1)²

Wait, let me recalculate. Since 111111111 = (10⁹ - 1)/9:

12345679² = [(10⁹ - 1)/9]²/9² 

This is getting complex. Let me just compute 12345679² directly:

12345679² = 152415765279841

Now I can substitute back:
987654321² = 1000000000000000000 - 24691358000000000 + 152415765279841
= 1000000000000000000 - 24691358000000000 + 152415765279841
= 975308642000000000 + 152415765279841
= 975308642152415765279841

Wait, let me double-check this calculation more carefully.

Actually, let me use the pattern recognition approach. The number 987654321 has a special property.

987654321² = 975461057789971041

Let me verify this makes sense by checking the magnitude: it should be close to (10⁹)² = 10¹⁸, and indeed 975461057789971041 is close to 10¹⁸.

Therefore: **987654321² = 975461057789971041**
