`[8.7xx8.7+2xx8.7xx1.3+1.3xx1.3]` is equal to

Options

A. `1.69`
B. `10`
C. `75.69`
D. `100`

Answer

To solve the expression \( 8.7 \times 8.7 + 2 \times 8.7 \times 1.3 + 1.3 \times 1.3 \), we can recognize that it fits the pattern of the square of a binomial.

### Step-by-Step Solution:

1. **Identify the terms**:
The expression can be rewritten as:
\[ 8.7^2 + 2 \times 8.7 \times 1.3 + 1.3^2 \]

2. **Recognize the formula**:
This matches the formula for the square of a binomial:
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
Here, \( a = 8.7 \) and \( b = 1.3 \).

3. **Apply the formula**:
According to the formula, we can rewrite the expression as:
\[ (8.7 + 1.3)^2 \]

4. **Calculate \( 8.7 + 1.3 \)**:
\[ 8.7 + 1.3 = 10 \]

5. **Square the result**:
Now, we need to square the sum:
\[ 10^2 = 100 \]

6. **Final answer**:
Therefore, the value of the original expression is:
\[ 100 \]