To multiply the two expressions \( (7 - \sqrt{2})(-2 - \sqrt{14}) \), we can use the distributive property (also known as the FOIL method for binomials):
\[ (7 - \sqrt{2})(-2 - \sqrt{14}) = 7 \cdot (-2) + 7 \cdot (-\sqrt{14}) - \sqrt{2} \cdot (-2) - \sqrt{2} \cdot (-\sqrt{14}) \]
Now calculate each term:
- \( 7 \cdot (-2) = -14 \)
- \( 7 \cdot (-\sqrt{14}) = -7\sqrt{14} \)
- \( -\sqrt{2} \cdot (-2) = 2\sqrt{2} \)
- \( -\sqrt{2} \cdot (-\sqrt{14}) = \sqrt{28} = 2\sqrt{7} \)
Combining all these results, we have:
\[ -14 - 7\sqrt{14} + 2\sqrt{2} + 2\sqrt{7} \]
Thus, the exact result of multiplying \( (7 - \sqrt{2})(-2 - \sqrt{14}) \) is:
\[ -14 - 7\sqrt{14} + 2\sqrt{2} + 2\sqrt{7} \]
This expression can be organized as:
\[ -14 + 2\sqrt{2} + 2\sqrt{7} - 7\sqrt{14} \]
If you need a specific option from the provided responses, none of them are a perfect match for this answer, but the closest representation based on the components might be useful in a particular context.