Question

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

Answer 1

To apply the Distributive Property to the expression \((7i - 8)(-2i - 5)\), we need to distribute each term in the first parenthesis by each term in the second parenthesis.

Here’s how it works step by step:

1. Distribute \(7i\) to both \(-2i\) and \(-5\):
- \(7i \cdot -2i = -14i^2\)
- \(7i \cdot -5 = -35i\)

2. Distribute \(-8\) to both \(-2i\) and \(-5\):
- \(-8 \cdot -2i = 16i\)
- \(-8 \cdot -5 = 40\)

Now we can combine all these results:

\[
(7i - 8)(-2i - 5) = -14i^2 - 35i + 16i + 40
\]

Next, combine the like terms (the \(i\) terms):

\[
-14i^2 + (-35i + 16i) + 40 = -14i^2 - 19i + 40
\]

Thus, the expression \((7i - 8)(-2i - 5)\) when simplified using the Distributive Property is:

\[
-14i^2 - 19i + 40
\]