To apply the Distributive Property to the expression \( (7i - 8)(-2i - 5) \), we need to distribute each term in the first binomial to each term in the second binomial.
Let's run through the steps:
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Distribute \( 7i \): \[ 7i \cdot (-2i) = -14i^2 \] \[ 7i \cdot (-5) = -35i \]
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Distribute \( -8 \): \[ -8 \cdot (-2i) = 16i \] \[ -8 \cdot (-5) = 40 \]
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Combine all the results: \[ -14i^2 - 35i + 16i + 40 \]
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Combine like terms: \[ -14i^2 + (-35i + 16i) + 40 = -14i^2 - 19i + 40 \]
So, the expression \( (7i - 8)(-2i - 5) \) when applying the Distributive Property simplifies to:
\[ -14i^2 - 19i + 40 \]