Expand the following:
$(3 a-2 b)^{3}$
Prove that $(a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a).$
Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by
$x+3$
Examine whether $2 x+3$ is a factor of $2 x^{3}+21 x^{2}+67 x+60$ or not.
The following expressions are polynomials? Justify your answer:
$\frac{1}{5 x^{-2}}+5 x+7$