To apply the Distributive Property to the expression \((7i - 8)(-2i - 5)\), we will distribute each term in the first expression by each term in the second expression. Here’s how it works:
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Distribute \(7i\) to both terms in \((-2i - 5)\):
- \(7i \cdot (-2i) = -14i^2\)
- \(7i \cdot (-5) = -35i\)
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Distribute \(-8\) to both terms in \((-2i - 5)\):
- \(-8 \cdot (-2i) = 16i\)
- \(-8 \cdot (-5) = 40\)
Now we can combine all the results: \[ -14i^2 - 35i + 16i + 40 \]
Next, combine like terms:
- Combine the \(i\) terms: \(-35i + 16i = -19i\)
So, the final expression after applying the Distributive Property is: \[ -14i^2 - 19i + 40 \]
Thus, this is the correct application of the Distributive Property to the expression \((7i - 8)(-2i - 5)\).