Question : Simplify the following expression.
$(4 x + 1)^2 - (4 x + 3)(4 x - 1)$

Option 1: $(4 x + 1)$

Option 2: $4$

Option 3: $(4x- 3)$

Option 4: $4x$

Question : If $(x–4)(x^2+4x+16)=x^3–p$, then $p$ is equal to:

Option 1: 27

Option 2: 8

Option 3: 64

Option 4: 0

Question : What is the LCM of $\left(8 x^3+80 x^2+200 x\right)$ and $\left(4 x^4+16 x^3-20 x^2\right)$?

Option 1: $8 x^2(x+5)^2(x-1)$

Option 2: $8 x^2(x-1)^2(x+5)$

Option 3: $4 x^2(x-1)^2(x+5)$

Option 4: $4 x^2(x+5)^2(x-1)$

Question : If $x^2-8 x-1=0$, what is the value of $x^2+\frac{1}{x^2}?$

Option 1: 68

Option 2: 62

Option 3: 64

Option 4: 66

Question : If $x=a+\frac{1}{a}$ and $y=a-\frac{1}{a}$, then the value of $x^4+y^4-2x^2y^2$ is:

Option 1: 4

Option 2: 8

Option 3: 16

Option 4: 64