I'll compute 987654321² systematically.

## Setting Up the Calculation

Let me write 987654321 = 1,000,000,000 - 12,345,679

Wait, let me verify: 1,000,000,000 - 987,654,321 = 12,345,679 ✓

## Using (a - b)² = a² - 2ab + b²

Where a = 10⁹ and b = 12,345,679

**a²** = 10¹⁸ = 1,000,000,000,000,000,000

**2ab** = 2 × 10⁹ × 12,345,679 = 24,691,358 × 10⁹ = 24,691,358,000,000,000

**b²** = 12,345,679²

### Computing 12,345,679²

12,345,679 = 12,000,000 + 345,679

- (12,000,000)² = 144,000,000,000,000
- 2 × 12,000,000 × 345,679 = 24 × 345,679 × 10⁶ = 8,296,296 × 10⁶ = 8,296,296,000,000
- (345,679)² = ?

345,679² : (345,000 + 679)²
- 345,000² = 119,025,000,000
- 2 × 345,000 × 679 = 468,510,000
- 679² = 461,041
- Sum: 119,025,000,000 + 468,510,000 + 461,041 = **119,493,971,041**

So b² = 144,000,000,000,000 + 8,296,296,000,000 + 119,493,971,041
= **152,415,789,971,041**

## Final Assembly

$$a^2 - 2ab + b^2$$

```
  1,000,000,000,000,000,000
-        24,691,358,000,000,000
+           152,415,789,971,041
```

Step 1: 1,000,000,000,000,000,000 - 24,691,358,000,000,000 = **975,308,642,000,000,000**

Step 2: 975,308,642,000,000,000 + 152,415,789,971,041 = **975,461,057,789,971,041**

## Result

$$987{,}654{,}321^2 = \boxed{975{,}461{,}057{,}789{,}971{,}041}$$
