Question

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

Answer 1

To apply the Distributive Property to the expression \( (7i - 8)(-2i - 5) \), we need to distribute each term in the first binomial to each term in the second binomial.

Let's run through the steps:

1. **Distribute \( 7i \):**
\[
7i \cdot (-2i) = -14i^2
\]
\[
7i \cdot (-5) = -35i
\]

2. **Distribute \( -8 \):**
\[
-8 \cdot (-2i) = 16i
\]
\[
-8 \cdot (-5) = 40
\]

3. **Combine all the results:**
\[
-14i^2 - 35i + 16i + 40
\]

4. **Combine like terms:**
\[
-14i^2 + (-35i + 16i) + 40 = -14i^2 - 19i + 40
\]

So, the expression \( (7i - 8)(-2i - 5) \) when applying the Distributive Property simplifies to:

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