Suppose I have got this polynomial
Now, I am trying to collect this polynomial with x^4 terms. I need to write it like this: (-1+x^4) (-3 + x^4) (1 + x^4)
To evaluate it, I used
(-1 + x) (1 + x) (1 + x^2) (-3 + x^4) (1 + x^4)
Collect[%, x^4, Simplify]
3 - x^4 - 3 x^8 + x^12
But, finally I am not able to reach what I need. Could anyone help me to solve this problem?