Find the products: `(x-1/x)\ (x+1/x)(x^2+1/(x^2))\ (x^4+1/(x^4))`

Explanation

To find the product \((x - \frac{1}{x})(x + \frac{1}{x})(x^2 + \frac{1}{x^2})(x^4 + \frac{1}{x^4})\), we can use algebraic identities step by step.

### Step 1: Multiply the first two terms
We start with \((x - \frac{1}{x})(x + \frac{1}{x})\). This resembles the identity \(a^2 - b^2\), where \(a = x\) and \(b = \frac{1}{x}\).

Using the identity:
\[
(x - \frac{1}{x})(x + \frac{1}{x}) = x^2 - \left(\frac{1}{x}\right)^2 = x^2 - \frac{1}{x^2}
...