Select the correct answer.

Shawn is packing these two boxes with food collected during his school's canned food drive.

Which expression represents the total volume of the two boxes?

A. [tex]$84x^3 - 282x^2 - 138x - 336$[/tex]

B. [tex]$27x^3 + 48x^2 - 99x$[/tex]

C. [tex]$21x^3 - 48x^2 - 199x$[/tex]

D. [tex]$13x^2 + 20x - 57$[/tex]

To determine which expression represents the total volume of the two boxes, we need to sum the polynomial expressions of each box's volume and then compare the resultant expression with the given choices. Here’s a step-by-step breakdown:

1. First Box Volume:
[tex]\[84x^3 - 282x^2 - 138x - 336\][/tex]

2. Second Box Volume:
[tex]\[27x^3 + 48x^2 - 99x\][/tex]

3. Combine the two expressions:
[tex]\[
\begin{aligned}
& (84x^3 - 282x^2 - 138x - 336) + (27x^3 + 48x^2 - 99x) \\
&= 84x^3 + 27x^3 - 282x^2 + 48x^2 - 138x - 99x - 336
\end{aligned}
\][/tex]

4. Combine like terms:
[tex]\[
\begin{aligned}
& (84x^3 + 27x^3) + (-282x^2 + 48x^2) + (-138x - 99x) - 336 \\
&= 111x^3 - 234x^2 - 237x - 336
\end{aligned}
\][/tex]

5. Compare the combined expression with the given options:
- [tex]$84x^3 - 282x^2 - 138x - 336$[/tex]
- [tex]$27x^3 + 48x^2 - 99x$[/tex]
- [tex]$21x^3 - 48x^2 - 199x$[/tex]
- [tex]$13x^2 + 20x - 57$[/tex]

The combined expression [tex]$111x^3 - 234x^2 - 237x - 336$[/tex] is the sum of the two initial box volumes.

Thus, the correct answer is:

[tex]\[ \boxed{84x^3 - 282x^2 - 138x - 336 + 27x^3 + 48x^2 - 99x} \][/tex]