Which of the following shows the expression (4i − 3)(−2i + 2)

Question

completely simplified using the Distributive Property?(1 point)
Responses

−12
negative 12

2+14i
2 plus 14 i

−8i2+14i−6
negative 8 i squared plus 14 i minus 6

14+2i

Answer 1

To simplify the expression \((4i - 3)(-2i + 2)\) using the Distributive Property (also known as FOIL for two binomials), we follow these steps:

1. Distribute each term in the first binomial by each term in the second binomial:

   \(4i \cdot -2i = -8i^2\)

   \(4i \cdot 2 = 8i\)

   \(-3 \cdot -2i = 6i\)

   \(-3 \cdot 2 = -6\)

2. Combine all the products:

   \(-8i^2 + 8i + 6i - 6\)

   Combine like terms:

   • The imaginary parts: \(8i + 6i = 14i\)

   So, we get: \(-8i^2 + 14i - 6\)

Therefore, the completely simplified expression is:

−8i^2 + 14i − 6

This corresponds to the option: negative 8 i squared plus 14 i minus 6.