`8^4-8^2=?`

Options

A. 64
B. 512
C. 4032
D. 4096

Answer

To solve the expression \( 8^4 - 8^2 \), we can follow these steps:

### Step 1: Factor out the common term
We notice that both terms in the expression share a common factor of \( 8^2 \). We can factor \( 8^2 \) out of the expression:

\[ 8^4 - 8^2 = 8^2(8^2 - 1) \]

### Step 2: Simplify the expression inside the parentheses
Next, we simplify the expression inside the parentheses:

\[ 8^2 - 1 \]

We know that \( 8^2 = 64 \), so:

\[ 8^2 - 1 = 64 - 1 = 63 \]

### Step 3: Substitute back into the factored expression
Now we substitute back into our factored expression:

\[ 8^2(8^2 - 1) = 8^2 \cdot 63 \]

### Step 4: Calculate \( 8^2 \)
We already calculated \( 8^2 \):

\[ 8^2 = 64 \]

### Step 5: Multiply the results
Now we multiply \( 64 \) by \( 63 \):

\[ 64 \cdot 63 \]

To calculate \( 64 \cdot 63 \), we can break it down:

\[ 64 \cdot 63 = 64 \cdot (60 + 3) = 64 \cdot 60 + 64 \cdot 3 \]

Calculating each part:

\[ 64 \cdot 60 = 3840 \]
\[ 64 \cdot 3 = 192 \]

Now add these two results together:

\[ 3840 + 192 = 4032 \]

### Final Answer
Thus, the final answer is:

\[ 8^4 - 8^2 = 4032 \]

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