Question

Find the product: ( x-1/x ) ( x+1/x ) ( x2+1/x2 ) ( x4+1/x4 )

Answer 1

Use the difference of 2 squares (a - b)(a + b) = a^2 - b^2:-

(x - 1/x)(x + 1/x) = x^2 - (1/x)^2

= x^2 - 1/x^2

(x ^2 - 1/x^2)(x^2 + 1 /x^2)

= x^4 - 1/x^4

(x^4 - 1/x^4)(x^4 + 1/x^4)

= x^8 - 1 /x^8 Answer