Find the factors of $(a-b)^{3}+(b-c)^{3}+(c-a)^{3}$.

Resolve into factors: $16 x^{2}-72 x y+81 y^{2}-12 x+27 y$

When a polynomial $f(x)$ is divided by $x-3$ and $x+6,$ the respective remainders are $7$ and $22.$ What is the remainder when $f(x)$ is divided by $(x-3)(x+6)?$

If $x = \sqrt[3]{x^{2} + 11} - 2$,then the value of $(x^{3} + 5x^{2} + 12x)$ is

If $a+b+c=0,$ then the value of $\left(\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}\right)$ is:

Factorize: $45 a^{3} b + 5 a b^{3} - 30 a^{2} b^{2}$