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Sagot :
Answer:
Let's simplify the given expression step by simplify
\[
(8 - 3^i) - (8 - 3^i)(8 + 8^i)
\]
First, let's distribute in the second term:
\[
(8 - 3^i) - (8 - 3^i)(8 + 8^i)
\]
We can rewrite the second term using the distributive property:
\[
(8 - 3^i) - [8(8 + 8^i) - 3^i(8 + 8^i)]
\]
Next, let's distribute inside the brackets:
\[
8(8 + 8^i) = 8 \cdot 8 + 8 \cdot 8^i = 64 + 8 \cdot 8^i
\]
\[
-3^i(8 + 8^i) = -3^i \cdot 8 - 3^i \cdot 8^i
\]
Combine these:
\[
8(8 + 8^i) - 3^i(8 + 8^i) = 64 + 8 \cdot 8^i - 3^i \cdot 8 - 3^i \cdot 8^i
\]
Now substitute back into the original expression:
\[
(8 - 3^i) - (64 + 8 \cdot 8^i - 3^i \cdot 8 - 3^i \cdot 8^i)
\]
Distribute the negative sign:
\[
(8 - 3^i) - 64 - 8 \cdot 8^i + 3^i \cdot 8 + 3^i \cdot 8^i
\]
Now combine like terms:
\[
8 - 3^i - 64 - 8 \cdot 8^i + 3^i \cdot 8 + 3^i \cdot 8^i
\]
Reorganize to see if any terms cancel out:
\[
8 - 64 - 3^i + 3^i \cdot 8 - 8 \cdot 8^i + 3^i \cdot 8^i
\]
Simplify:
\[
8 - 64 - 3^i + 8 \cdot 3^i - 8 \cdot 8^i + 3^i \cdot 8^i
\]
Combine like terms:
\[
-56 + 5 \cdot 3^i - 8 \cdot 8^i + 3^i \cdot 8^i
\]
The final simplified form of the expression is:
\[
-56 + 5 \cdot 3^i - 8 \cdot 8^i + 3^i \cdot 8^i
\]
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