Question

Which of the following correctly shows the application of the Distributive Property to the expression (7i−8)(−2i−5) ?(1 point)
Responses

54−19i
54 minus 19 i

−54+19i
negative 54 plus 19 i

36−19i
36 minus 19 i

−36+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.

1. Distributing \( 7i \):
- \( 7i \cdot (-2i) = -14i^2 \)
- \( 7i \cdot (-5) = -35i \)

2. Distributing \( -8 \):
- \( -8 \cdot (-2i) = 16i \)
- \( -8 \cdot (-5) = 40 \)

Now, combine all these results together:

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

Combine like terms (\(-35i + 16i = -19i\)):

\[
-14i^2 - 19i + 40
\]

Since \( i^2 = -1 \), we know \( -14i^2 = 14 \).

Thus, our expression simplifies to:

\[
14 - 19i + 40 = 54 - 19i
\]

From the options provided, the correct application of the Distributive Property is:

**54 − 19i** (54 minus 19i).