Factorise the following:

$9 x^{2}+4 y^{2}+16 z^{2}+12 x y-16 y z-24 x z$

If both $x-2$ and $x-\frac{1}{2}$ are factors of $p x^{2}+5 x+r,$ show that $p=r$

Expand

$(x+4)(x+9)$

Prove that $(a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a).$

Factorise $: 8 x^{3}+y^{3}-27 z^{3}+18 x y z$