Use the Distributive Property to simplify (6−3i)(3−5i) .(1 point)

Question

Responses

33−39i
33 minus 39 i

3−39i
3 minus 39 i

9−8i
9 minus 8 i

18+15i2

Answer 1

To simplify \((6 - 3i)(3 - 5i)\) using the Distributive Property (also known as the FOIL method for binomials), we do the following steps:

1. First: Multiply the first terms:
   \(6 \cdot 3 = 18\)

2. Outer: Multiply the outer terms:
   \(6 \cdot (-5i) = -30i\)

3. Inner: Multiply the inner terms:
   \((-3i) \cdot 3 = -9i\)

4. Last: Multiply the last terms:
   \((-3i) \cdot (-5i) = 15i^2\)
   Since \(i^2 = -1\), this becomes \(15(-1) = -15\).

Now, combine all these results: \[ 18 - 30i - 9i - 15 \]

Combine like terms: \[ (18 - 15) + (-30i - 9i) = 3 - 39i \]

Thus, the simplified expression is: \[ 3 - 39i \]

The correct response is: 3−39i.