To solve the expression [tex]\((8 - 3i) - (8 - 3i)(8 + 8i)\)[/tex], we will simplify the components step-by-step.
First, compute the product [tex]\((8 - 3i) \cdot (8 + 8i)\)[/tex]:
1. Apply the distributive property (also known as the FOIL method):
[tex]\[
\begin{align*}
(8 - 3i)(8 + 8i) &= 8 \cdot 8 + 8 \cdot 8i - 3i \cdot 8 - 3i \cdot 8i \\
&= 64 + 64i - 24i - 24i^2
\end{align*}
\][/tex]
2. Simplify the expression by combining like terms and remembering that [tex]\(i^2 = -1\)[/tex]:
[tex]\[
\begin{align*}
64 + 64i - 24i - 24(-1) &= 64 + 40i + 24 \\
&= 88 + 40i
\end{align*}
\][/tex]
Now, subtract this product from the original complex number [tex]\((8 - 3i)\)[/tex]:
[tex]\[
(8 - 3i) - (88 + 40i)
\][/tex]
3. Distribute the negative sign:
[tex]\[
\begin{align*}
(8 - 3i) - (88 + 40i) &= 8 - 3i - 88 - 40i \\
&= 8 - 88 - 3i - 40i \\
&= -80 - 43i
\end{align*}
\][/tex]
Therefore, the value of the expression [tex]\((8 - 3i) - (8 - 3i)(8 + 8i)\)[/tex] is:
[tex]\[
\boxed{-80 - 43i}
\][/tex]
Thus, the correct answer is:
A. [tex]\(-80 - 43i\)[/tex]
