If x = a + 1/a and y = a - 1/a, then the value of x4 + y4 - 2x2y2 is?

Answer: Option C

$$\begin{array}{rl}& x=a+\frac{1}{a}\\ & x^2=a^2+\frac{1}{a^2}+2\\ & y^2=a^2+\frac{1}{a^2}-2\\ & \text{Now, }\\ & x^4+y^4-2x^2{y}^2\\ & ={\left(x^2-y^2\right)}^2\\ & ={\left(a^2+\frac{1}{a^2}+2-a^2-\frac{1}{a^2}+2\right)}^2\\ & ={\left(4\right)}^2\\ & =16\end{array}$$