Question : Simplify the given expression.
$(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)$

Option 1: $2y(x - 3y)$

Option 2: $2y(x + 3y)$

Option 3: $2x(x - 3y)$

Option 4: $2x(x + 3y)$

Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?

Option 1: 8

Option 2: 12

Option 3: 4

Option 4: 6

Question : If $x= 19$ and $y= 18$, then the value of $\frac{x^{2}+y^{2}+xy}{x^{3}-y^{3}}$ is:

Option 1: 1

Option 2: 37

Option 3: 324

Option 4: 361

Question : If $x^4+x^2 y^2+y^4=21$ and $x^2+xy+y^2=3$, then what is the value of $4xy $?
 

Option 1: –8

Option 2: 4

Option 3: –4

Option 4: 12

Question : What is the simplified value of:
$\frac{1}{8}\left\{\left(x+\frac{1}{y}\right)^2-\left(x-\frac{1}{y}\right)^2\right\}$

Option 1: $\frac{x}{y}$

Option 2: $\frac{2x}{y}$

Option 3: $\frac{x}{2y}$

Option 4: $\frac{4x}{y}$