In the problem that the student factored incorrectly, they left out a term. Even though you factored out 2xy, you still need to leave a 1 in its place, so you can distribute it back out. If you distribute out the incorrectly factored equation, you will get 6x^9y^2. If you distribute out 2xy(3x^8y+1), you will get 6x^9y^2+2xy.
