`a^3-0.064`

Answer

To factor the expression \( a^3 - 0.064 \), we can follow these steps:

### Step 1: Identify the expression as a difference of cubes
The expression \( a^3 - 0.064 \) can be recognized as a difference of cubes. We can rewrite \( 0.064 \) as \( (0.4)^3 \) because \( 0.4 \times 0.4 \times 0.4 = 0.064 \).

### Step 2: Use the difference of cubes formula
The difference of cubes formula states that:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]
In our case, \( a = a \) and \( b = 0.4 \).

### Step 3: Substitute into the formula
Substituting \( a \) and \( b \) into the formula, we get:
\[ a^3 - (0.4)^3 = (a - 0.4)(a^2 + a(0.4) + (0.4)^2) \]

### Step 4: Simplify the expression
Now, we simplify the second factor:
- \( a^2 \) remains as it is.
- \( a(0.4) = 0.4a \).
- \( (0.4)^2 = 0.16 \).

Putting it all together, we have:
\[ a^3 - 0.064 = (a - 0.4)(a^2 + 0.4a + 0.16) \]

### Final Answer
Thus, the factored form of \( a^3 - 0.064 \) is:
\[ (a - 0.4)(a^2 + 0.4a + 0.16) \]

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