Find the intervals in which `f(x)={x(x-2)}^2` is increasing or decreasing.

Explanation

To determine the intervals in which the function \( f(x) = (x(x-2))^2 \) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative \( f'(x) \)
To find the intervals of increase and decrease, we first need to compute the derivative of the function.

1. Rewrite the function:
\[
f(x) = (x^2 - 2x)^2
...