Explanation

Given:

(1+x)(1+x2)(1+x4)(1+x8)(1−x),

$$$$(1+x)(1+x2)(1+x4)(1+x8)(1−x)

This is a well-known identity in algebra that builds up as a geometric progression product:

Identity:

(1−x)(1+x)(1+x^2)(1+x^4)(1+x^8)=1−x^16

$$$$(1−x)(1+x)(1+x2)(1+x4)(1+x8)=1−x16

So,

(1+x)(1+x^2)(1+x^4)(1+x^8)(1−x)=1−x^16

$$$$(1+x)(1+x2)(1+x4)(1+x8)(1−x)=1−x16