Which of the following correctly shows the application of the Distributive Property to the expression (7i−8)(−2i−5) ?(1 point) Responses 36−19i 36 minus 19 i −36+19i negative 36 plus 19 i −54+19i negative 54 plus 19 i 54−19i

Answer 1

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.

Let's break it down step by step:

\[ (7i - 8)(-2i - 5) = 7i \cdot (-2i) + 7i \cdot (-5) - 8 \cdot (-2i) - 8 \cdot (-5) \]

Now calculate each term:

1. \(7i \cdot (-2i) = -14i^2\)
2. \(7i \cdot (-5) = -35i\)
3. \(-8 \cdot (-2i) = 16i\)
4. \(-8 \cdot (-5) = 40\)

Now, combine these results:

\[ -14i^2 - 35i + 16i + 40 \]

Since \(i^2 = -1\), we can substitute:

\[ -14(-1) - 35i + 16i + 40 = 14 - 35i + 16i + 40 \]

Now, combine the like terms:

\[ 14 + 40 + (-35i + 16i) = 54 - 19i \]

Thus, the final simplified expression is:

\[ 54 - 19i \]

The correct option is:

54 - 19i