I need to compute 987654321².

I'll use the identity (a - b)² = a² - 2ab + b², where a = 987654321.

Let me instead compute this directly by breaking it up. Let me use the fact that 987654321 = 10⁹ - 12345679.

Wait, let me verify: 10⁹ - 12345679 = 999999999 - 12345679 = 987654320. That's off by 1.

Let me try: 987654321 = 10⁹ - 12345679? 
999999999 - 987654321 = 12345678. So 987654321 = 10⁹ - 1 - 12345678 = 999999999 - 12345678.

Let me just use (10⁹ - 12345679)² ... actually that equals 987654320, not 987654321.

Let me use a = 1000000000 - 12345679 = 987654321? Check: 1000000000 - 12345679 = 987654321. Yes!

So 987654321 = 10⁹ - 12345679.

987654321² = (10⁹)² - 2 × 10⁹ × 12345679 + 12345679²

= 10¹⁸ - 24691358 × 10⁹ + 12345679²

Now I need 12345679². Let me compute this:
12345679² = (12345679)²

12345679 × 12345679. Let me use (12000000 + 345679)²:
= 144000000000000 + 2 × 12000000 × 345679 + 345679²
= 144000000000000 + 8296296000000 + 345679²

345679² = Let me compute: (345000 + 679)² = 119025000000 + 2×345000×679 + 679²
= 119025000000 + 468510000 + 461041
= 119493971041

So 12345679² = 144000000000000 + 8296296000000 + 119493971041
= 152296296000000 + 119493971041
= 152415789971041

Let me verify: 12345679 × 12345679. Actually, there's a known fact that 12345679 × 9 = 111111111. Let me verify: 12345679 × 9 = 111,111,111. Yes!

So 12345679 = 111111111/9

12345679² = 111111111²/81 = 12345678987654321/81

111111111² = 12345678987654321 (this is a known identity).
12345678987654321 / 81 = let me compute: 81 × 152415789... 
81 × 152415789971041 = ?

Let me just use my computed value: 12345679² = 152415789971041.

Now: 987654321² = 10¹⁸ - 24691358000000000 + 152415789971041

10¹⁸ = 1000000000000000000
-24691358000000000 = gives 975308642000000000
+152415789971041

975308642000000000 + 152415789971041 = 975461057789971041

Wait, let me redo this addition carefully:
975308642000000000
+    152415789971041

975308642000000000
+152415789971041

= 975,308,642,000,000,000 + 152,415,789,971,041

= 975,461,057,789,971,041

Let me verify this makes sense. 987654321² should have 18 digits. 975461057789971041 has 18 digits. ✓

Let me double-check with a small verification: 987654321 × 987654321 mod 9. 
987654321: digit sum = 9+8+7+6+5+4+3+2+1 = 45, so ≡ 0 mod 9.
So the answer should be ≡ 0 mod 9.
9+7+5+4+6+1+0+5+7+7+8+9+9+7+1+0+4+1 = 90 ≡ 0 mod 9. ✓

**987654321² = 975,461,057,789,971,041**
