What is the simplified value of $$\ (x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x-\frac{1}{x})(x^{16}+\frac{1}{x^{16}})(x+\frac{1}{x})(x^{4}+\frac{1}{x^{4}})$$?

Expression = $$\ (x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x-\frac{1}{x})(x^{16}+\frac{1}{x^{16}})(x+\frac{1}{x})(x^{4}+\frac{1}{x^{4}})$$

= $$\ (x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^2-\frac{1}{x^2})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})$$

Multiply and divide by $$(x^2+\frac{1}{x^2})$$, we get :

= $$\frac{1}{x^2+\frac{1}{x^2}}\times\ (x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^2-\frac{1}{x^2})(x^2+\frac{1}{x^2})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})$$

= $$\frac{1}{x^2+\frac{1}{x^2}}\times\ (x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})(x^4-\frac{1}{x^4})$$

= $$\frac{1}{x^2+\frac{1}{x^2}}\times\ (x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^{16}+\frac{1}{x^{16}})(x^{8}-\frac{1}{x^{8}})$$

= $$\frac{1}{x^2+\frac{1}{x^2}}\times\ (x^{32}+\frac{1}{x^{32}})(x^{16}+\frac{1}{x^{16}})(x^{16}-\frac{1}{x^{16}})$$

= $$\frac{1}{x^2+\frac{1}{x^2}}\times\ (x^{32}+\frac{1}{x^{32}})(x^{32}-\frac{1}{x^{32}})$$

= $$\frac{1}{x^2+\frac{1}{x^2}}\times\ (x^{64}-\frac{1}{x^{64}})$$

=> Ans - (B)