Which of the following correctly shows the application of the Distributive Property to the expression (7i−8)(−2i−5) ?(1 point)

Question

Responses

54−19i
54 minus 19 i

36−19i
36 minus 19 i

−54+19i
negative 54 plus 19 i

−36+19i

Answer 1

To apply the Distributive Property (also known as the FOIL method for binomials) to the expression \((7i - 8)(-2i - 5)\), we will multiply each term in the first bracket by each term in the second bracket:

1. First: \(7i \cdot -2i = -14i^2\)
2. Outside: \(7i \cdot -5 = -35i\)
3. Inside: \(-8 \cdot -2i = 16i\)
4. Last: \(-8 \cdot -5 = 40\)

Now we combine these results:

\[ -14i^2 - 35i + 16i + 40 \]

Combine like terms:

• The imaginary terms: \(-35i + 16i = -19i\)
• The constant term remains the same: \(40\)
• Note that \(i^2 = -1\), so \(-14i^2 = 14\).

Now combine everything:

\[ 14 + 40 - 19i = 54 - 19i \]

So the correct application of the Distributive Property results in:

\[ 54 - 19i \]

The correct answer is:

54−19i