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

Answer 1

To simplify the expression \( 3i[(2i) + (-3i - 5)] \) using the Distributive Property, we follow these steps:

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

2. Substitute this back into the expression: \[ 3i[-i - 5]. \]

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

4. Calculate each term:

   • For \( 3i \cdot (-i) \): \[ 3i \cdot (-i) = -3i^2. \] Since \( i^2 = -1 \), this becomes: \[ -3(-1) = 3. \]
   • For \( 3i \cdot (-5) \): \[ 3i \cdot (-5) = -15i. \]

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

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