Evaluate

$(1002)^{2}$

The polynomial $p(x)=x^{4}-2 x^{3}+3 x^{2}-a x+3 a-7$ when divided by $x+1$ leaves the remainder $19 .$ Find the values of $a .$ Also find the remainder when $p(x)$ is divided by $x+2.$

Factorise :

$a^{3}-2 \sqrt{2} b^{3}$

Divide $p(x)=21+10 x+x^{2}$ by $g(x)=2+x$ and find the quotient and the remainder.

Find the following products:

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

If $p(x)=x^{2}-4 x+3,$ evaluate $: p(2)-p(-1)+p\left(\frac{1}{2}\right)$