Which of the following correctly shows the application of the Distributive Property to the expression (7i−8)(−2i−5) ?(1 point)
Responses
−54+19i
negative 54 plus 19 i
36−19i
36 minus 19 i
54−19i
54 minus 19 i
−36+19i
To apply the Distributive Property to the expression (7i - 8)(-2i - 5), we need to multiply each term in the first parenthesis by each term in the second parenthesis:
7i * -2i + 7i * -5 - 8 * -2i - 8 * -5
Simplifying:
-14i^2 - 35i + 16i + 40
Since i^2 = -1, we can rewrite -14i^2 as 14:
14 - 35i + 16i + 40
Combining like terms:
54 - 19i
Therefore, the correct answer is 54 - 19i.