I'll multiply these two large numbers step by step.

Let me break this down using the standard multiplication algorithm:

123456789123456789 × 987654321987654321

I'll work through this systematically:

123456789123456789 × 987654321987654321

Let me use the fact that both numbers have a pattern. I can write:
- First number: 123456789123456789 = 123456789 × 10^9 + 123456789
- Second number: 987654321987654321 = 987654321 × 10^9 + 987654321

Using the formula (a×10^9 + a)(b×10^9 + b) = ab×10^18 + 2ab×10^9 + ab = ab(10^18 + 2×10^9 + 1)

Where a = 123456789 and b = 987654321

First, let me calculate a × b = 123456789 × 987654321:

123456789 × 987654321 = 121932631137021929

Now I need to multiply this by (10^18 + 2×10^9 + 1):

121932631137021929 × (10^18 + 2×10^9 + 1)

= 121932631137021929 × 10^18 + 121932631137021929 × 2 × 10^9 + 121932631137021929

= 121932631137021929000000000000000000 + 243865262274043858000000000 + 121932631137021929

Adding these together:

121932631137021929000000000000000000
+            243865262274043858000000000
+                     121932631137021929
= 121932631381887191274043858121932631137021929

Therefore:
123456789123456789 × 987654321987654321 = 121932631381887191274043858121932631137021929
