`1299 xx1299 = ?`

Options

A. 1585301
B. 1684701
C. 1685401
D. 1687401

Answer

To solve the problem \( 1299 \times 1299 \), we can use the formula for the square of a binomial. Specifically, we can express \( 1299 \) as \( 1300 - 1 \).

### Step-by-Step Solution:

1. **Rewrite the Expression:**
\[ 1299 \times 1299 = (1300 - 1) \times (1300 - 1) \]

2. **Apply the Binomial Square Formula:**
The formula for \( (A - B)^2 \) is:
\[ A^2 - 2AB + B^2 \]
Here, let \( A = 1300 \) and \( B = 1 \).

3. **Calculate Each Term:**
- Calculate \( A^2 \):
\[ 1300^2 = 1690000 \]
- Calculate \( B^2 \):
\[ 1^2 = 1 \]
- Calculate \( 2AB \):
\[ 2 \times 1300 \times 1 = 2600 \]

4. **Combine the Results:**
Substitute these values back into the formula:
\[ 1299^2 = A^2 - 2AB + B^2 = 1690000 - 2600 + 1 \]

5. **Perform the Subtraction and Addition:**
- First, subtract \( 2600 \) from \( 1690000 \):
\[ 1690000 - 2600 = 1687400 \]
- Then add \( 1 \):
\[ 1687400 + 1 = 1687401 \]

6. **Final Result:**
Thus, the final answer is:
\[ 1299 \times 1299 = 1687401 \]

### Summary of the Steps:
- Rewrite the number as \( 1300 - 1 \).
- Use the binomial square formula.
- Calculate \( A^2 \), \( B^2 \), and \( 2AB \).
- Substitute back into the formula and simplify.