Find the product `100008xx100004`.

Options

A. 1000120032
B. 10001200032
C. 1100120032
D. 12001200332

Answer

To find the product of \( 100008 \times 100004 \), we can use the distributive property of multiplication to simplify the calculation. Here are the steps:

### Step 1: Rewrite the numbers
We can express the numbers in a more manageable form:
\[ 100008 = 100000 + 8 \]
\[ 100004 = 100000 + 4 \]

### Step 2: Apply the distributive property
Now we can multiply these two expressions:
\[ 100008 \times 100004 = (100000 + 8)(100000 + 4) \]

Using the distributive property (also known as the FOIL method for binomials), we expand this:
\[ = 100000 \times 100000 + 100000 \times 4 + 8 \times 100000 + 8 \times 4 \]

### Step 3: Calculate each term
Now we calculate each term:
1. \( 100000 \times 100000 = 10000000000 \)
2. \( 100000 \times 4 = 400000 \)
3. \( 8 \times 100000 = 800000 \)
4. \( 8 \times 4 = 32 \)

### Step 4: Sum all the terms
Now we add all these results together:
\[ 10000000000 + 400000 + 800000 + 32 \]

Combining the terms:
\[ 10000000000 + 400000 + 800000 = 10000800000 \]
Now add \( 32 \):
\[ 10000800000 + 32 = 10000800032 \]

### Final Answer
Thus, the product \( 100008 \times 100004 = 100012000032 \).

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