Question : The third proportional of the following numbers $(x-y)^2, (x^2-y^2)^2$ is:

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

Option 2: $(x+y)^4(x-y)^2$

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

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

Question : Simplify the given expression $\frac{(x^3-y^3)(x+y)}{x^2+x y+y^2}$.

Option 1: $x - y$

Option 2: $x^2-y^2$

Option 3: $x + y$

Option 4: $x^2+y^2$

Question : The third proportional to $\left(x^2-y^2\right)$ and $(x-y)$ is:

Option 1: $(x -y)$

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

Option 3: $\frac{x+y}{x-y}$

Option 4: $(x + y)$

Question : $\left(4 x^3 y-6 x^2 y^2+4 x y^3-y^4\right)$ can be expressed as:

Option 1: $(x+y)^4-x^4$

Option 2: $(x+y)^4-y^4$

Option 3: $(x-y)^4-x^4$

Option 4: $x^4-(x-y)^4$

Question : What is the simplified value of $\frac{(x+y+z)(x y+y z+z x)–x y z}{(x+y)(y+z)(z+x)}$?

Option 1: $y$

Option 2: $z$

Option 3: $1$

Option 4: $x$