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

Options

A. `0.0092`
B. `0.092`
C. `0.00092`
D. None of the above

Answer

To find the value of the expression \(0.096 \times 0.096 - 0.004 \times 0.004\), we can use the difference of squares formula, which states that:

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

### Step 1: Identify \(a\) and \(b\)
In our case, we can identify:
- \(a = 0.096\)
- \(b = 0.004\)

### Step 2: Write the expression using the difference of squares
Using the difference of squares formula, we can rewrite the expression as:

\[ 0.096^2 - 0.004^2 = (0.096 + 0.004)(0.096 - 0.004) \]

### Step 3: Calculate \(a + b\) and \(a - b\)
Now, we calculate \(a + b\) and \(a - b\):

1. \(a + b = 0.096 + 0.004 = 0.1\)
2. \(a - b = 0.096 - 0.004 = 0.092\)

### Step 4: Substitute back into the expression
Now we substitute these values back into the expression:

\[ (0.1)(0.092) \]

### Step 5: Multiply the two results
Now, we multiply \(0.1\) and \(0.092\):

\[ 0.1 \times 0.092 = 0.0092 \]

### Final Answer
Thus, the value of the expression \(0.096 \times 0.096 - 0.004 \times 0.004\) is:

\[ \boxed{0.0092} \]