Write the degree of the following polynomial: $x^{8}-6561$.

Which of the following expressions is a polynomial,and state the reason? If an expression is a polynomial,state whether it is a polynomial in one variable or not: $x^{3}+3 x^{2} y+3 x y^{2}+y^{3}$

Find the value of the following polynomial at the indicated value of the variable:
$q(y) = 5y^3 - 4y^2 + 14y - \sqrt{3}$ at $y = 2$

Give an example of a polynomial,which is:
$(i)$ monomial of degree $1$
$(ii)$ binomial of degree $20$
$(iii)$ trinomial of degree $2$

From the following polynomials,find out which of them has $(x+1)$ as a factor:
$p(x) = x^{3} - 5x^{2} + 2x + 8$

Expand $\left(\frac{x}{2}-\frac{2}{5}\right)^{2}$.