To apply the Distributive Property to the expression \((7i−8)(−2i−5)\), we need to distribute each term in the first expression to each term in the second expression. Let's break it down step by step.
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Distribute \(7i\):
- \(7i \cdot (-2i) = -14i^2\)
- \(7i \cdot (-5) = -35i\)
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Distribute \(-8\):
- \(-8 \cdot (-2i) = 16i\)
- \(-8 \cdot (-5) = 40\)
Now, we combine all these results:
- The resulting expression is: \[ -14i^2 - 35i + 16i + 40 \]
Now, combine like terms:
- Combine the \(i\) terms: \(-35i + 16i = -19i\)
- The \(i^2\) term simplifies to \( -14i^2\) but since \(i^2 = -1\), this equals \(14\).
Thus, the expression becomes: \[ 14 - 19i + 40 \] Combine the constant terms: \[ 54 - 19i \]
After combining everything, we find that the final answer is: \[ 54 - 19i \]
Therefore, the correct response from the choices given is: 54 - 19i.