How do i factor 15AsquaredBcubed+10AsquaredBsquared-5ABcubed?
$\displaystyle 15A^2B^3+10A^2B^2+5AB^3$
In each bit you can divide by 5 without leaving any remainder.
You can also see there's an $\displaystyle A$ in each bit.
Also, there's a $\displaystyle B$ in each bit. In fact, there's at least 2 $\displaystyle B$'s in each bit.
So you can extract a 5, an $\displaystyle A$ and two $\displaystyle B$'s.
This gives, for each bit:
$\displaystyle 5AB^2 \times 3AB$
$\displaystyle 5AB^2 \times 2A$
$\displaystyle 5AB^2 \times B$
So putting it all together we get:
$\displaystyle 5AB^2 (3AB + 2A + B)$.