Math Expression Interpretation

The problem requires evaluating the mathematical expression (999) 2 - 2 2. The notation can be interpreted in a few ways, but considering the given options, the most likely meaning is that (999) 2 represents $999^2$ (999 squared) and 2 2 represents $2 \times 2$ (2 multiplied by 2).

$999^2$ Calculation

To calculate $999^2$, we can represent 999 as $(1000 - 1)$. Using the algebraic identity $(a - b)^2 = a^2 - 2ab + b^2$, where $a = 1000$ and $b = 1$:

$$ 999^2 = (1000 - 1)^2 $$

Applying the formula:

$$ 999^2 = 1000^2 - (2 \times 1000 \times 1) + 1^2 $$

$$ 999^2 = 1000000 - 2000 + 1 $$

$$ 999^2 = 998001 $$

$2 \times 2$ Evaluation

The second part of the expression, 2 2, is interpreted as $2 \times 2$.

$$ 2 \times 2 = 4 $$

Final Math Calculation

Now, we substitute the calculated values back into the expression and perform the subtraction:

$$ 999^2 - (2 \times 2) = 998001 - 4 $$

$$ 998001 - 4 = 997997 $$

Result Confirmation

The final result of the calculation is $997997$. This matches the fourth option presented.