What is the value of the following?

​$$(a+1)(1-a)(1-a+a^2)(1+a+a^2)(1+a^6)$$​​​

Correct option is D

Given:​

​$$(a+1)(1-a)(1-a+a^2)(1+a+a^2)(1+a^6)$$

Formula Used:​

a³ + b³ = (a + b) (a² - ab + b²)

a³ - b³ = (a - b) (a² + ab + b²)

a² - b²=(a + b) (a - b)

Solution:​

​$$[(a+1)(1-a+a^2)][(1-a)(1+a+a^2)](1+a^6)$$

=$$[(1+a)(1-a+a^2)](1-a^3)(1+a^6)$$​​

=$$(1+a^3)(1-a^3)(1+a^6)$$

= (1 - a⁶)(1 + a^6​)

= 1 - a¹²​