Find the value of the expression
`0.096 xx 0.096 - 0.004 xx 0.004`

Options

A. `0.0092`
B. `0.092`
C. `0.92`
D. None of the above

Answer

To solve the expression \(0.096 \times 0.096 - 0.004 \times 0.004\), we can follow these steps:

### Step 1: Rewrite the expression
We can rewrite the expression using the square notation:
\[ 0.096^2 - 0.004^2 \]

### Step 2: Identify the difference of squares
This expression is in the form of a difference of squares, which can be factored using the formula:
\[ a^2 - b^2 = (a - b)(a + b) \]
Here, \(a = 0.096\) and \(b = 0.004\).

### Step 3: Apply the difference of squares formula
Using the difference of squares formula, we can rewrite the expression as:
\[ (0.096 - 0.004)(0.096 + 0.004) \]

### Step 4: Calculate \(0.096 - 0.004\) and \(0.096 + 0.004\)
Now, we calculate each part:
\[ 0.096 - 0.004 = 0.092 \]
\[ 0.096 + 0.004 = 0.100 \]

### Step 5: Multiply the results
Now we multiply the two results:
\[ 0.092 \times 0.100 \]

### Step 6: Perform the multiplication
Calculating this gives:
\[ 0.092 \times 0.100 = 0.0092 \]

### Final Answer
Thus, the value of the expression \(0.096 \times 0.096 - 0.004 \times 0.004\) is:
\[ \boxed{0.0092} \]

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