Factorise :

$8x^3+27y^3+36x^{2}y+54x{y}^2$

If $A, B$ and $C$ are three points on a line, and $B$ lies between $A$ and $C$ (see Fig), then prove that $AB+BC=AC$.

In Fig., lines $PQ$ and $RS$ intersect each other at point $O$. If $\angle POR:\angle ROQ=5:7$, find all the angles.

In Fig., ray $OS$ stands on a line $POQ$. Ray $OR$ and ray $OT$ are angle bisectors of $\angle POS$ and $\angle SOQ$, respectively. If $\angle POS=x$, find $\angle ROT$.

In Fig., $OP, OQ, OR$ and $OS$ are four rays. Prove that $\angle P\mathrm{OQ}+\angle QOR+\angle SOR+\angle POS=360°$.

In Fig, if $PQ\parallel RS, \angle MXQ=135°$ and $\angle MYR=40°$, find $\angle XMY$.