Without actually calculating the cubes, find the value of each of the following

$(21)^{3}+(15)^{3}+(-36)^{3}$

Write whether the following statements are True or False. Justify your answer.

$\frac{1}{\sqrt{5}} x^{\frac{1}{2}}+1$ is a polynomial

Which of the following expressions is a polynomial, state the reason ? If an expression is polynomial, state whether it is a polynomial in one variable or not

$\sqrt{3} x^{2}+\pi x-9$

Write the degree of each of the following polynomials

$a x^{3}+b x^{2}+c x+d$

Factorise :

$a^{3}-8 b^{3}-64 c^{3}-24 a b c$

Expand the following:

$\left(4-\frac{1}{3 x}\right)^{3}$