Factorise each of the following
$27 x^{3}-8 y^{3}-54 x^{2} y+36 x y^{2}$
$(3 x-2 y)(3 x-2 y)(3 x-2 y)$
Expand
$\left(x-\frac{1}{2}\right)^{2}$
The following expressions are polynomials? Justify your answer:
$8$
$(2 a+3 b)^{2}$
If $p(x)=x^{4}-2 x^{3}+3 x^{2}-a x+3 a-7$ is divided by $(x+1),$ then the remainder is $19 .$ Find the value of a. Also, find the remainder, when $p(x)$ is divided by $(x+2)$
Evaluate
$(421)^{2}$
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