Find the value of `0.064 xx 0.064 + 2 xx 0.064 xx 99.936 + 99.936 xx 99.936`

Options

A. 100
B. 1000
C. 9999
D. None of these

Answer

To solve the expression \(0.064 \times 0.064 + 2 \times 0.064 \times 99.936 + 99.936 \times 99.936\), we can use the algebraic identity for the square of a binomial.

### Step-by-Step Solution:

1. **Identify the terms in the expression**:
We have three terms:
- \(0.064 \times 0.064\) (which can be written as \(0.064^2\))
- \(2 \times 0.064 \times 99.936\)
- \(99.936 \times 99.936\) (which can be written as \(99.936^2\))

2. **Recognize the algebraic identity**:
The expression can be recognized as:
\[ a^2 + 2ab + b^2 \]
where \(a = 0.064\) and \(b = 99.936\). This matches the form of the identity:
\[ (a + b)^2 = a^2 + 2ab + b^2 \]

3. **Rewrite the expression using the identity**:
Therefore, we can rewrite the expression as:
\[ (0.064 + 99.936)^2 \]

4. **Calculate the sum inside the parentheses**:
\[ 0.064 + 99.936 = 100 \]

5. **Square the result**:
Now we square the sum:
\[ (100)^2 = 10000 \]

6. **Final Result**:
The value of the expression \(0.064 \times 0.064 + 2 \times 0.064 \times 99.936 + 99.936 \times 99.936\) is:
\[ 10000 \]