`a^3+0.008`

Answer

To factor the expression \( a^3 + 0.008 \), we can recognize that \( 0.008 \) can be expressed as \( (0.2)^3 \). Therefore, we can rewrite the expression as:

\[ a^3 + (0.2)^3 \]

This expression can be factored using the sum of cubes formula, which states:

\[ x^3 + y^3 = (x + y)(x^2 - xy + y^2) \]

In our case, let \( x = a \) and \( y = 0.2 \). Now we can apply the formula:

1. **Step 1**: Identify \( x \) and \( y \).
- Here, \( x = a \) and \( y = 0.2 \).

2. **Step 2**: Apply the sum of cubes formula.
- Using the formula, we have:
\[ a^3 + (0.2)^3 = (a + 0.2)(a^2 - a(0.2) + (0.2)^2) \]

3. **Step 3**: Simplify the second factor.
- Calculate \( a^2 - a(0.2) + (0.2)^2 \):
\[ a^2 - 0.2a + 0.04 \]

4. **Step 4**: Combine the results.
- Therefore, the complete factorization of \( a^3 + 0.008 \) is:
\[ (a + 0.2)(a^2 - 0.2a + 0.04) \]

So, the final answer is:

\[ a^3 + 0.008 = (a + 0.2)(a^2 - 0.2a + 0.04) \]