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

May 4, 2015

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: $2 {x}^{3} + 4 {x}^{2} y$
Group 2: $- 2 {x}^{2} - 4 x y$

Factor out $2 {x}^{2}$ in the first group, getting
$2 {x}^{2} \left(x + 2 y\right)$
Factor out $- 2 x$ in the second group, getting
$- 2 x \left(x + 2 y\right)$

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