`9997 xx 10003=?`

Options

A. 9999991
B. 99999911
C. 99999991
D. 9999911

Answer

To solve the multiplication of \(9997 \times 10003\), we can use the algebraic identity for the difference of squares. Here’s a step-by-step breakdown of the solution:

### Step 1: Rewrite the numbers
We can express \(9997\) and \(10003\) in terms of \(10000\):
- \(9997 = 10000 - 3\)
- \(10003 = 10000 + 3\)

### Step 2: Use the difference of squares formula
The multiplication can be rewritten using the identity \( (a - b)(a + b) = a^2 - b^2 \):
- Let \(a = 10000\) and \(b = 3\).
- Thus, \(9997 \times 10003 = (10000 - 3)(10000 + 3) = 10000^2 - 3^2\).

### Step 3: Calculate \(10000^2\)
Now, we calculate \(10000^2\):
- \(10000^2 = 100000000\).

### Step 4: Calculate \(3^2\)
Next, we calculate \(3^2\):
- \(3^2 = 9\).

### Step 5: Subtract the squares
Now we subtract \(3^2\) from \(10000^2\):
- \(100000000 - 9 = 99999991\).

### Conclusion
Thus, the result of \(9997 \times 10003\) is:
\[ \boxed{99999991} \]