Question

(X-1/x)(x+1/x)(x×x-1/x×x)(x×x×x×x+1/x×x×x×x)​

Answer 1

(x^4+1/x^4)(x^2+1/x^2)(x+1/x)(x-1/x)

= (x^4+1/x^4)(x^2+1/x^2)(x^2-1/x^2)

let, x^2= a

so, (a^2+1/a^2)(a+1/a)(a-1/a)

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

let , a^2= b

so, (b+1/b)(b-1/b)

=b^2-1/b^2

= (a^2)^2-1/(a^2)^2

=a^4 -. 1/a^4

= (x^2)^4 - 1/(x^2)^4

= x^8 - 1/x^8

Answer 2

Answer:

Step-by-step explanation:

(x^4+1/x^4)(x^2+1/x^2)(x+1/x)(x-1/x)

= (x^4+1/x^4)(x^2+1/x^2)(x^2-1/x^2)

let, x^2= a

so, (a^2+1/a^2)(a+1/a)(a-1/a)

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

let , a^2= b

so, (b+1/b)(b-1/b)

=b^2-1/b^2

= (a^2)^2-1/(a^2)^2

=a^4 -. 1/a^4

= (x^2)^4 - 1/(x^2)^4

= x^8 - 1/x^8