Fractorise:
` x ^(3) - 64x`

Answer

To factorize the expression \( x^3 - 64x \), we can follow these steps:

### Step 1: Identify the common factor
The expression \( x^3 - 64x \) has a common factor of \( x \).

### Step 2: Factor out the common factor
We can factor out \( x \) from the expression:
\[ x^3 - 64x = x(x^2 - 64) \]

### Step 3: Recognize the difference of squares
Now, we notice that \( x^2 - 64 \) is a difference of squares. It can be expressed as:
\[ x^2 - 64 = x^2 - 8^2 \]

### Step 4: Apply the difference of squares formula
Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we can factor \( x^2 - 8^2 \):
\[ x^2 - 8^2 = (x - 8)(x + 8) \]

### Step 5: Combine the factors
Now we can combine all the factors we have:
\[ x(x^2 - 64) = x(x - 8)(x + 8) \]

### Final Answer
Thus, the fully factored form of \( x^3 - 64x \) is:
\[ \boxed{x(x - 8)(x + 8)} \]

---