Question : If $x - y = 8$ and $8xy = 8$, then what is the value of $2 x^3-2 y^3$?

Option 1: 536

Option 2: 1092

Option 3: 1072

Option 4: 1608

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

Option 1: 24

Option 2: 4

Option 3: 16

Option 4: 8

Question : If ${x^2+y^2+z^2=2(x+z-1)}$, then the value of $x^3+y^3+z^3$ is equal to:

Option 1: 6

Option 2: 1

Option 3: 2

Option 4: 8

Question : If $\frac{x^2-1}{x}=8$, then what is the value of $\frac{x^6-1}{x^3}=?$

Option 1: 496

Option 2: 536

Option 3: 512

Option 4: 488

Question : If $x^3=270+y^3$ and $x=(6+y)$, then what is the value of $(x+y)? $(given that $x>0$ and $y>0$)

Option 1: $2 \sqrt{3}$

Option 2: $\sqrt{3}$

Option 3: $4 \sqrt{3}$

Option 4: $4 \sqrt{2}$

Question : If $\tan (x + y)=1$ and $\cos (x-y)={\frac{\sqrt3}{2}}$, then what is the value of $x$ and $y$?

Option 1: $x = 3^\circ, y = 4.5^\circ$

Option 2: $x = 37.5^\circ, y = 7.5^\circ$

Option 3: $x = 7.5^\circ, y = 37.5^\circ$

Option 4: $x = 4.5^\circ, y = 3^\circ$