A teacher gives the following expression to his students to solve.
`25 xx 25 +2 xx 25 xx 36 + 36 xx 36`
Which of the following method is appropriate to solve the expression shortly?

Options

A. Using the square of(a+b)
B. Using the square of (a-b)
C. Using the cube of (a + b)
D. Using the cube of (a - b)

Answer

To solve the expression \( 25 \times 25 + 2 \times 25 \times 36 + 36 \times 36 \) efficiently, we can recognize that it resembles the expansion of the square of a binomial. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the expression**:
The expression given is:
\[ 25 \times 25 + 2 \times 25 \times 36 + 36 \times 36 \]

2. **Rewrite using variables**:
Let \( a = 25 \) and \( b = 36 \). Then, we can rewrite the expression as:
\[ a^2 + 2ab + b^2 \]

3. **Recognize the formula**:
The expression \( a^2 + 2ab + b^2 \) is the expansion of \( (a + b)^2 \). Therefore, we can express it as:
\[ (a + b)^2 \]

4. **Substitute back the values of \( a \) and \( b \)**:
Now substitute \( a \) and \( b \) back into the expression:
\[ (25 + 36)^2 \]

5. **Calculate the sum**:
Calculate \( 25 + 36 \):
\[ 25 + 36 = 61 \]

6. **Square the result**:
Now square the sum:
\[ 61^2 = 3721 \]

### Final Answer:
Thus, the value of the expression \( 25 \times 25 + 2 \times 25 \times 36 + 36 \times 36 \) is \( 3721 \).