Question

find the product of using identity (a-1/2)(a+1/a)(a^2+1/a^2)(a^4+1/a^4)

Answer 1

using identity:
(x - y) (x + y) = x2 - y2

(a - 1/a)(a + 1/a) (a2 + 1/a2)(a4 + 1/a4)
= [(a)2 - (1/a)2] (a2 + 1/a2)(a4 + 1/a4)
= (a2 - 1/a2) (a2 + 1/a2)(a4 + 1/a4)
= [(a2)2 - (1/a2)2] (a4 + 1/a4)
= (a4 - 1/a4) (a4 + 1/a4)
= (a4)2 - (1/a4)2
= a8 - 1/a8

Answer 2

answer is a^8 -1/a^8