Question

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

Answer 1

To apply the Distributive Property to the expression \((7i - 8)(-2i - 5)\), we will distribute each term in the first expression by each term in the second expression. Here’s how it works:

1. Distribute \(7i\) to both terms in \((-2i - 5)\):
- \(7i \cdot (-2i) = -14i^2\)
- \(7i \cdot (-5) = -35i\)

2. Distribute \(-8\) to both terms in \((-2i - 5)\):
- \(-8 \cdot (-2i) = 16i\)
- \(-8 \cdot (-5) = 40\)

Now we can combine all the results:
\[
-14i^2 - 35i + 16i + 40
\]

Next, combine like terms:
- Combine the \(i\) terms: \(-35i + 16i = -19i\)

So, the final expression after applying the Distributive Property is:
\[
-14i^2 - 19i + 40
\]

Thus, this is the correct application of the Distributive Property to the expression \((7i - 8)(-2i - 5)\).