`(.58xx.58xx.58-.42xx.42xx.42-3xx.58xx.42xx.16)=?`

Options

A. 0.004096
B. 1.3976
C. 0.16
D. 1

Answer

To solve the expression \(0.58 \times 0.58 \times 0.58 - 0.42 \times 0.42 \times 0.42 - 3 \times 0.58 \times 0.42 \times 0.16\), we can follow these steps:

### Step 1: Calculate \(0.58^3\)
First, we need to calculate \(0.58 \times 0.58 \times 0.58\).

\[ 0.58 \times 0.58 = 0.3364 \]
\[ 0.3364 \times 0.58 = 0.195112 \]

### Step 2: Calculate \(0.42^3\)
Next, we calculate \(0.42 \times 0.42 \times 0.42\).

\[ 0.42 \times 0.42 = 0.1764 \]
\[ 0.1764 \times 0.42 = 0.074088 \]

### Step 3: Calculate \(3 \times 0.58 \times 0.42 \times 0.16\)
Now, we need to calculate \(3 \times 0.58 \times 0.42 \times 0.16\).

First, calculate \(0.58 \times 0.42\):
\[ 0.58 \times 0.42 = 0.2436 \]

Now, multiply by \(0.16\):
\[ 0.2436 \times 0.16 = 0.038976 \]

Now multiply by \(3\):
\[ 3 \times 0.038976 = 0.116928 \]

### Step 4: Combine the results
Now we can substitute the values back into the original expression:

\[ 0.195112 - 0.074088 - 0.116928 \]

### Step 5: Perform the subtraction
First, subtract \(0.074088\) from \(0.195112\):
\[ 0.195112 - 0.074088 = 0.121024 \]

Now subtract \(0.116928\):
\[ 0.121024 - 0.116928 = 0.004096 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{0.004096} \]

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