Question : Find the mean proportion of $x^3y$ and $xy^3$.

Option 1: $x^2y^2$

Option 2: $x^3y^3$

Option 3: $xy$

Option 4: $x^4 y^4$

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

Question : Simplify the given expression.
$(1 - 2x)^2 - (1 + 2x)^2$

Option 1: $8x$

Option 2: $-8x$

Option 3: $-(2 + 8x^2)$

Option 4: $2 + 8x^2$

Question : Simplify:
$(x+y)^3-(x-y)^3-6y(x^2-y^2)$

Option 1: $8y^3$

Option 2: $x^3$

Option 3: $8x^2$

Option 4: $y^3$

Question : Simplify the given expression: $(1 + x)^3 + (1 – x)^3 + (–2)^3$

Option 1: $6(1 - x^2)$

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

Option 3: $-6(1 - x^2)$

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