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What is the value of the expression given below? (8-3^i)-(8-3^i)(8+8^i)

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

\]