The value of `(5.71 xx 5.71 xx 5.71 - 2.79 xx 2.79 xx 2.79 )/( 5.71 xx 5.71 + 5.71 xx 2.79 xx 2.79 + 2.79 )` in simplified form is :

Options

A. `8.5`
B. `8.6`
C. `2.82`
D. `2.92`

Answer

To simplify the expression \((5.71 \times 5.71 \times 5.71 - 2.79 \times 2.79 \times 2.79) / (5.71 \times 5.71 + 5.71 \times 2.79 \times 2.79 + 2.79)\), we can follow these steps:

### Step 1: Define Variables
Let \( a = 5.71 \) and \( b = 2.79 \).

### Step 2: Rewrite the Expression
The expression can be rewritten using \( a \) and \( b \):
\[ \frac{a^3 - b^3}{a^2 + ab + b^2} \]

### Step 3: Apply the Difference of Cubes Formula
Recall the difference of cubes formula:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]
Thus, we can substitute this into our expression:
\[ \frac{(a - b)(a^2 + ab + b^2)}{a^2 + ab + b^2} \]

### Step 4: Simplify the Expression
Since \( a^2 + ab + b^2 \) is common in the numerator and denominator (and is not zero), we can cancel it out:
\[ a - b \]

### Step 5: Substitute Back the Values
Now substitute back the values of \( a \) and \( b \):
\[ 5.71 - 2.79 \]

### Step 6: Calculate the Result
Now perform the subtraction:
\[ 5.71 - 2.79 = 2.92 \]

### Final Answer
Thus, the value of the expression in simplified form is:
\[ \boxed{2.92} \]