# How do you factor #2x^3 -128x#?

##### 1 Answer

Oct 18, 2015

#### Explanation:

Start by breaking down your initial expression in search of possible *common factors*

#2x^3 = color(blue)(2 * x) * x^2#

#128x = 64 * color(blue)(2 * x)#

This means that you can use

#2x^3 - 128x = 2x * (x^2 - 64)#

Notice that **perfect square**

#64 = 8 * 8 = 8^2#

which means that you are actually dealing with the *difference of two squares*

#color(blue)(a^2 - b^2 = (a-b)(a+b))#

The bracket can thus be written as

#x^2 - 64 = x^2 - 8^2 = (x-8)(x+8)#

The expression will thus be equivalent to

#2x^3 - 128x = color(green)(2x(x-8)(x+8))#