To apply the Distributive Property to the expression \((7i - 8)(-2i - 5)\), we need to distribute each term in the first parenthesis by each term in the second parenthesis.
Here’s how it works step by step:
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Distribute \(7i\) to both \(-2i\) and \(-5\):
- \(7i \cdot -2i = -14i^2\)
- \(7i \cdot -5 = -35i\)
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Distribute \(-8\) to both \(-2i\) and \(-5\):
- \(-8 \cdot -2i = 16i\)
- \(-8 \cdot -5 = 40\)
Now we can combine all these results:
\[ (7i - 8)(-2i - 5) = -14i^2 - 35i + 16i + 40 \]
Next, combine the like terms (the \(i\) terms):
\[ -14i^2 + (-35i + 16i) + 40 = -14i^2 - 19i + 40 \]
Thus, the expression \((7i - 8)(-2i - 5)\) when simplified using the Distributive Property is:
\[ -14i^2 - 19i + 40 \]