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:
-
First: Multiply the first terms:
\( 7i \cdot -2i = -14i^2 \) -
Outside: Multiply the outer terms:
\( 7i \cdot -5 = -35i \) -
Inside: Multiply the inner terms:
\( -8 \cdot -2i = 16i \) -
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:
\[ -14i^2 - 19i + 40 \]
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