Question

How do you factor by grouping `2x^3 + 4x^2 y - 2x^2 - 4xy`?

Answer 1

Notice the similarity of the coefficients, 2, 4, -2, -4. It prompts to group the four terms of this expression into two groups:
Group 1: `2x^3+4x^2y`
Group 2: `-2x^2-4xy`

Factor out `2x^2` in the first group, getting
`2x^2(x+2y)`
Factor out `-2x` in the second group, getting
`-2x(x+2y)`

Now you see that `(x+2y)` is a common factor in both groups. Therefore, the original expression can be represented as:
`2x^2(x+2y)-2x(x+2y)=(2x^2-2x)(x+y)=2x(x-1)(x+2y)`