Evaluate
$(421)^{2}$
Evaluate using suitable identities : $(998)^{3}$
Expand
$(3 x+5)^{2}$
Factorise
$x^{2}+\frac{y^{2}}{4}+\frac{z^{2}}{16}+x y+\frac{y z}{4}+\frac{z x}{2}$
If the polynomial $a x^{3}+4 x^{2}+3 x-4$ and polynomial $x^{3}-4 x+a$ leave the same remainder when each is divided by $x-3,$ find the value of $a$.