Question 121499
The trick here is to recognise the given binomial expression as the difference of two cubes.
{{{512y^3-729 = (8y)^3-9^3}}}
The difference of two cubes can be factored nicely as follows:
{{{A^3-B^3 = (A-B)(A^2+AB+B^2)}}} so, applying this to your problem:
{{{512y^3-729 = (8y)^3-9^3}}}={{{(8y-9)((8y)^2+(8y)(9)+9^2)}}} Simplifying this we get:
{{{(8y-9)(64y^2+72y+81)}}}