I need to multiply 123456789123456789 × 987654321987654321.

Let me denote:
- A = 123456789
- B = 987654321

So I'm multiplying (A × 10^9 + A) × (B × 10^9 + B) = AB × 10^18 + AB × 10^9 + AB × 10^9 + AB
= AB × 10^18 + 2AB × 10^9 + AB
= AB × (10^18 + 2×10^9 + 1)

First, let me calculate A × B = 123456789 × 987654321.

Breaking this down:
123456789 × 987654321

I'll compute this step by step:
- 123456789 × 900000000 = 111111110100000000
- 123456789 × 87654321

For 123456789 × 87654321:
- 123456789 × 80000000 = 9876543120000000
- 123456789 × 7654321

For 123456789 × 7654321:
- 123456789 × 7000000 = 864197523000000
- 123456789 × 654321

For 123456789 × 654321:
- 123456789 × 654321 = 80779853369469

Let me use a more systematic approach:
123456789 × 987654321

= 123456789 × 987654321
= 121932631112635269

Let me verify: A × B = 121932631112635269

Now I need: AB × (10^18 + 2×10^9 + 1)

= 121932631112635269 × 10^18 + 2 × 121932631112635269 × 10^9 + 121932631112635269

= 121932631112635269000000000000000000
+    243865262225270538000000000
+            121932631112635269

Adding these:
```
121932631112635269000000000000000000
          243865262225270538000000000
                  121932631112635269
```

Result: **121932631356500531347203169112635269**
