Evaluate: `(0.6 xx 0.6 xx 0.6- 0.3 xx 0.3 xx 0.3)/(0.6 xx 0.6 + 0.6 xx 0.3 + 0.3 xx 0.3)`, using suitable identity

Answer

To evaluate the expression \((0.6 \times 0.6 \times 0.6 - 0.3 \times 0.3 \times 0.3) / (0.6 \times 0.6 + 0.6 \times 0.3 + 0.3 \times 0.3)\), we can use the identity for the difference of cubes and the sum of cubes.

### Step-by-step Solution:

1. **Identify the cubes**:
We can rewrite the expression as:
\[ \frac{0.6^3 - 0.3^3}{0.6^2 + 0.6 \times 0.3 + 0.3^2} \]

2. **Apply the difference of cubes formula**:
The difference of cubes can be factored using the identity:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]
Here, let \(a = 0.6\) and \(b = 0.3\). Thus, we have:
\[ 0.6^3 - 0.3^3 = (0.6 - 0.3)(0.6^2 + 0.6 \times 0.3 + 0.3^2) \]

3. **Substitute back into the expression**:
Substitute this back into our expression:
\[ \frac{(0.6 - 0.3)(0.6^2 + 0.6 \times 0.3 + 0.3^2)}{0.6^2 + 0.6 \times 0.3 + 0.3^2} \]

4. **Cancel out the common terms**:
The \(0.6^2 + 0.6 \times 0.3 + 0.3^2\) in the numerator and denominator cancels out:
\[ 0.6 - 0.3 \]

5. **Calculate the final result**:
Now, we compute:
\[ 0.6 - 0.3 = 0.3 \]

Thus, the final answer is:
\[ \boxed{0.3} \]