Factorise each of the following

$27 x^{3}-8 y^{3}-54 x^{2} y+36 x y^{2}$

Factorise :

$a^{3}-2 \sqrt{2} b^{3}$

With the help of the remainder theorem. find the remainder when the polynomial $x^{3}+7 x^{2}+17 x+25$ is divided by $x+4$

Which of the following expressions are polynomials in one variable and which are not $?$ State reason for your answer. If the given expression is a polynomial, state whether it is a polynomial in one variable or not

$x^{3}+y^{3}+z^{3}-3 x y z$

Write the coefficient of $x^{2}$ in each of the following:

$(i)$ $\frac{\pi}{6} x+x^{2}-1$

$(ii)$ $3 x-5$

Find $p(0), p(1), p(-2)$ for the following polynomials:

$p(y)=(y+2)(y-2)$