To apply the Distributive Property to the expression \( (7i - 8)(-2i - 5) \), we need to distribute each term in the first parentheses to each term in the second parentheses.
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Distributing \( 7i \):
- \( 7i \cdot (-2i) = -14i^2 \)
- \( 7i \cdot (-5) = -35i \)
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Distributing \( -8 \):
- \( -8 \cdot (-2i) = 16i \)
- \( -8 \cdot (-5) = 40 \)
Now, combine all these results together:
\[ -14i^2 - 35i + 16i + 40 \]
Combine like terms (\(-35i + 16i = -19i\)):
\[ -14i^2 - 19i + 40 \]
Since \( i^2 = -1 \), we know \( -14i^2 = 14 \).
Thus, our expression simplifies to:
\[ 14 - 19i + 40 = 54 - 19i \]
From the options provided, the correct application of the Distributive Property is:
54 − 19i (54 minus 19i).