Question

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

Answer 1

To apply the Distributive Property to the expression \(3i[(2i) + (-3i - 5)]\), we first simplify the expression inside the brackets.

1. **Simplify the expression inside the brackets**:
\[
(2i) + (-3i - 5) = 2i - 3i - 5 = -i - 5
\]

2. **Rewrite the expression**:
\[
3i[-i - 5]
\]

3. **Apply the Distributive Property**:
\[
3i \cdot (-i) + 3i \cdot (-5)
\]

4. **Calculate each term**:
- For the first term:
\[
3i \cdot (-i) = -3i^2
\]
Since \(i^2 = -1\), we have:
\[
-3i^2 = -3(-1) = 3
\]

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

5. **Combine the results**:
\[
3 - 15i
\]

So, the expression \(3i[(2i) + (-3i - 5)]\) in its simplest form is:
\[
\boxed{3 - 15i}
\]