How do you factor #4+3xy6y2x# by grouping?
1 Answer
The answer would be (3y2)(x2) .
Explanation:

Arrange the equation with like terms near each other.
3xy  6y 2x + 4 
Look for the GCF between the first two terms (i.e. a common factor, like y, that you can separate out). In this example we can see that 3xy and 6y have a GCF of y and 3. This is justified because y is a factor in both, and 6 is evenly divided by three, thus three is a factor of both. Take out the GCF.
3y(x  2)  2x + 4 
In order to group you need to be able to take out a GCF of two groups in order to make them the same base. For example, since I now have (x  2) as a factor, in order to group I need to make sure that the 2x + 4 becomes (x  2). I can right away see that 2x + 4 has a GCF of 2. So I take out the two to get: 2(x + 2). However, note that (x2) is different than (x+2). Thus our work is not done.

Take out a negative GCF. This is a common solution to reverse signs in a factor when grouping. I simply add a negative sign to the 2 in 2(x + 2), and because I am dividing by a negative, all the signs in the factor flip. Thus: 2(x  2).

Now I have two factors that are the same, so I combine them to one, and then group the GCFs into a factor of their own. Thus:
(3y  2)(x  2)