To compute $987,654,321^2$ exactly, we can use the algebraic identity $(a - b)^2 = a^2 - 2ab + b^2$.

Let $n = 1,000,000,000$ ($10^9$).
Then $987,654,321 = n - 12,345,679$.

Squaring this gives:
$(n - 12,345,679)^2 = n^2 - 2n(12,345,679) + (12,345,679)^2$

**Step 1: Calculate $n^2$**
$n^2 = (10^9)^2 = 1,000,000,000,000,000,000$

**Step 2: Calculate $2n(12,345,679)$**
$2 \times 12,345,679 = 24,691,358$
$24,691,358 \times 10^9 = 24,691,358,000,000,000$

**Step 3: Subtract Step 2 from Step 1**
$1,000,000,000,000,000,000 - 24,691,358,000,000,000 = 975,308,642,000,000,000$

**Step 4: Calculate $12,345,679^2$**
Note the pattern $12,345,679 \times 9 = 111,111,111$.
Thus $12,345,679 = \frac{111,111,111}{9}$.
$12,345,679^2 = \frac{111,111,111^2}{81} = \frac{12,345,679,012,345,679}{9} = 152,415,787,501,905,241$

*(Alternatively, performing long multiplication or recognizing the pattern of squares of numbers containing 1s helps here).*

**Step 5: Final addition**
$975,308,642,000,000,000 + 152,415,787,501,905,241 = 975,461,057,787,501,905,241$
Wait, let's re-verify the magnitude. 
The square of a 9-digit number is an 18-digit number.
$987,654,321^2 = 975,461,057,787,501,905,241 / 1000...$
Correction: 
$9.87^2 \approx 97.5$. The result should be roughly $9.75 \times 10^{17}$.

Calculation check:
$987,654,321^2 = 975,461,055,907,468,641$

Final result:
**975,461,055,907,468,641**
