# How do you factor by grouping: x^3 - 2x^2 - 4x + 8?

Apr 21, 2015

To factor this expression, we can make groups of two like this:

$\left({x}^{3} - 2 {x}^{2}\right) - \left(4 x - 8\right)$

$= {x}^{2} \left(x - 2\right) - 4 \left(x - 2\right)$

The factor $x - 2$ is common to both the terms

$= \left(x - 2\right) \left({x}^{2} - 4\right)$

$= \left(x - 2\right) \left({x}^{2} - {2}^{2}\right)$

We also know that color(blue)(a^2 - b^2 = (a+b)(a-b)

$= \left(x - 2\right) \left(x + 2\right) \left(x - 2\right)$

color(green)( = (x - 2)^2*(x+2) is the factorised form of ${x}^{3} - 2 {x}^{2} - 4 x + 8$