To find the value of the expression (1+x)(1+x2)(1+x4)(1+x8)(1−x),
- 1+x ^16
- 1−x ^16
- x ^16 −1
- None of these
Explanation
Given:
(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
So,
(1+x)(1+x^2)(1+x^4)(1+x^8)(1−x)=1−x^16
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