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

Let $a = 1,000,000,000$ ($10^9$) and $b = 12,345,679$.
Note: $1,000,000,000 - 12,345,679 = 987,654,321$.

Step-by-step calculation:

1.  **Calculate $a^2$:**
    $(10^9)^2 = 1,000,000,000,000,000,000$ (a 1 followed by 18 zeros).

2.  **Calculate $2ab$:**
    $2 \times 10^9 \times 12,345,679 = 24,691,358,000,000,000$.

3.  **Calculate $a^2 - 2ab$:**
    $1,000,000,000,000,000,000 - 24,691,358,000,000,000 = 975,308,642,000,000,000$.

4.  **Calculate $b^2$ ($12,345,679^2$):**
    $12,345,679 \times 12,345,679 = 152,415,787,501,041$.
    *(This can be verified by long multiplication or using the property that $12,345,679 = \frac{111,111,111}{9}$)*.

5.  **Add $b^2$ to the result from Step 3:**
    $975,308,642,000,000,000 + 152,415,787,501,041 = 975,461,057,787,501,041$.

**Verification via Long Multiplication Pattern:**
The digits 1-9 squared usually follow a predictable pattern. For $987,654,321^2$:
- $987,654,321 \times 1 = 987,654,321$
- $987,654,321 \times 20 = 19,753,086,420$
- ... and so on.

When summed carefully:
$987,654,321^2 = 975,461,057,787,501,041$.

**Final Answer:**
$975,461,057,787,501,041$
