Question

Apply the Distributive Property to show 3i(2i−3i−5)
in its simplest form.(1 point)
Responses

3+15i
3 plus 15 i

6−15i
6 minus 15 i

3−15i
3 minus 15 i

6+15i

Answer 1

To simplify \( 3i(2i - 3i - 5) \) using the Distributive Property, follow these steps:

1. First, simplify the expression inside the parentheses:
\[
2i - 3i - 5 = -i - 5
\]

2. Now distribute \( 3i \) to each term in the expression:
\[
3i(-i) + 3i(-5)
\]

3. Calculate each term:
\[
3i(-i) = -3i^2
\]
Since \( i^2 = -1 \), we have:
\[
-3i^2 = -3(-1) = 3
\]

4. For the second term:
\[
3i(-5) = -15i
\]

5. Now combine the results:
\[
3 - 15i
\]

Thus, \( 3i(2i - 3i - 5) \) simplifies to **3 - 15i**.

The correct response is:
**3 - 15i**.