Factorise

$27 x^{3}-y^{3}+64 z^{3}+36 x y z$

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

Expand

$(3 x-1)(3 x+4)$

If $x+1$ is a factor of $a x^{3}+x^{2}-2 x+4 a-9,$ find the value of $a$.

If $a+b+c=5$ and $a b+b c+c a=10,$ then prove that $a^{3}+b^{3}+c^{3}-3 a b c=-25.$