Question

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

Answer 1

To simplify the expression \( 3i[(2i) + (-3i - 5)] \), we'll use the Distributive Property. This property states that \( a(b + c) = ab + ac \).

1. First, simplify the expression inside the brackets:
\[
2i + (-3i - 5) = 2i - 3i - 5 = -i - 5
\]

2. Now, substitute this back into the expression:
\[
3i[(-i - 5)]
\]

3. Now, distribute \( 3i \) to both terms inside the brackets:
\[
3i \cdot (-i) + 3i \cdot (-5)
\]

4. Calculate each term:
- For \( 3i \cdot (-i) \):
\[
= -3i^2
\]
Since \( i^2 = -1 \), this becomes:
\[
= -3(-1) = 3
\]

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

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

The simplest form of the expression \( 3i[(2i) + (-3i - 5)] \) is:
\[
3 - 15i
\]

So the correct final answer is \( \boxed{3 - 15i} \).