What is the value of the following expression:

​$$(1+x)(1+x^2)(1+x^4)(1+x^8)(1-x)$$​​

Correct option is A

Given:

The expression is $$(1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 - x).$$​​

Formula Used:
(a + b)(a - b) = a² - b²​

Solution:

​$$(1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 - x).$$​
​$$= (1 - x^2)(1 + x^2)(1 + x^4)(1 + x^8)$$

$$= (1 - x^4)(1 + x^4)(1 + x^8)$$

$$= (1 - x^8)(1 + x^8)$$​​

​$$= 1 - x^{16}.$$​​