Question

Which of the following correctly shows the application of the distributive property to the expression (7i-8)(-2i-5)

Answer 1

The distributive property states that \( a(b + c) = ab + ac \). To apply the distributive property to the expression \( (7i - 8)(-2i - 5) \), we will use the FOIL method (First, Outside, Inside, Last) since we are dealing with a binomial multiplication.

Here’s how it works step by step:

1. **First**: Multiply the first terms:
\( 7i \cdot -2i = -14i^2 \)

2. **Outside**: Multiply the outer terms:
\( 7i \cdot -5 = -35i \)

3. **Inside**: Multiply the inner terms:
\( -8 \cdot -2i = 16i \)

4. **Last**: Multiply the last terms:
\( -8 \cdot -5 = 40 \)

Now, combine all these results together:
\[ -14i^2 - 35i + 16i + 40 \]

Next, simplify the expression by combining like terms:
\[ -14i^2 + (-35i + 16i) + 40 \]
\[ -14i^2 - 19i + 40 \]

Thus, the result of applying the distributive property to the expression \( (7i - 8)(-2i - 5) \) is:
\[ -14i^2 - 19i + 40 \]