`123 xx 123 + 77 xx 77 + 2 xx 123 xx 77 = ?`

Answer

To solve the expression \( 123 \times 123 + 77 \times 77 + 2 \times 123 \times 77 \), we can recognize that it resembles the expansion of the square of a binomial. The formula for the square of a binomial is:

\[ (a + b)^2 = a^2 + b^2 + 2ab \]

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
- Let \( a = 123 \)
- Let \( b = 77 \)

2. **Rewrite the expression**:
- The expression can be rewritten as:
\[ a^2 + b^2 + 2ab \]

3. **Substitute \( a \) and \( b \)**:
- Substitute \( a \) and \( b \) into the formula:
\[ 123^2 + 77^2 + 2 \times 123 \times 77 \]

4. **Apply the binomial square formula**:
- This can be simplified to:
\[ (123 + 77)^2 \]

5. **Calculate \( 123 + 77 \)**:
- Calculate the sum:
\[ 123 + 77 = 200 \]

6. **Square the result**:
- Now, square the result:
\[ 200^2 = 40000 \]

### Final Answer:
Thus, the value of the expression \( 123 \times 123 + 77 \times 77 + 2 \times 123 \times 77 \) is \( 40000 \).

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