Question

find the product of (x-1/X)(X+1/X)(x^2+1/x2)(x^4+1/x^4)​

Answer 1

To make the simple form, take x = A and 1/x = B

Then we get $(A-B)(A+B)(A^2+B^2)(A^4+B^4)$

Now we use appropriate identity to simplify it.

→ $(A-B)(A+B)(A^2+B^2)(A^4+B^4)$

→ $(A^2-B^2)(A^2+B^2)(A^4+B^4)$

→ $(A^4-B^4)(A^4+B^4)$

→ $A^8-B^8$

→ $x^8-\frac{1}{x^8}$

The product is $x^8-\frac{1}{x^8}$