I am understanding whats going on so far generally but I have two specific questions. We will use this example from the book $\displaystyle 2x^4-6x-x^3y+3y = 2x(x{^3}-3)-y(x^3-3)=(2x-y)(x^3-3)

$

1.Typically, How can you tell it can be solved by grouping? I can do this method provided the header tells me "solve by grouping" but odds are if a factor grouping problem was put into a test randomly with other factoring problems I wouldnt be able to spot it.

2. I cant seem to remember why at this point $\displaystyle 2x(x{^3}-3)-y(x^3-3)$ the two $\displaystyle (x^{3}-3) $ merge into one. Why are we able to do this again?

Many thanks