Without actual division, prove that $2 x^{4}-5 x^{3}+2 x^{2}-x+2$ is divisible by $x^{2}-3 x+2$

Without finding the cubes, factorise

$(x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3}$

Evaluate $66 \times 74$ without directly multiplying

Expand

$\left(\frac{2 x}{3}+\frac{3 y}{4}\right)^{2}$

Check whether $p(x)$ is a multiple of $g(x)$ or not, where

$p(x)=x^{3}-x+1, \quad g(x)=2-3 x$