Question

Which of the following correctly shows the application of the Distributive Property to the expression (7i−8)(−2i−5)?(1 point)%0D%0AResponses%0D%0A%0D%0A36−19i%0D%0A36 minus 19 i%0D%0A%0D%0A−36+19i%0D%0Anegative 36 plus 19 i%0D%0A%0D%0A−54+19i%0D%0Anegative 54 plus 19 i%0D%0A%0D%0A54−19i

Answer 1

To apply the Distributive Property to the expression \((7i−8)(−2i−5)\), we can use the FOIL method (First, Outside, Inside, Last) to multiply the binomials.

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, combine these results:

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

Combine like terms:

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

Since \(i^2 = -1\), we have:

\[ -14(-1) - 19i + 40 = 14 - 19i + 40 = 54 - 19i \]

So, the final result is:

\[ 54 - 19i \]

Thus, the correct application of the Distributive Property to the expression \((7i−8)(−2i−5)\) is:

54 − 19i.