# How do you factor #2x^3-125#?

##### 1 Answer

Jun 24, 2017

#### Explanation:

The difference of cubes identity can be written:

#a^3-b^3 = (a-b)(a^2+ab+b^2)#

Note that

We can treat it as a cube by using irrational coefficients, to find:

#2x^3 = (root(3)(2)x)^3#

and hence:

#2x^3-125 = (root(3)(2)x)^3-5^3#

#color(white)(2x^3-125) = (root(3)(2)x-5)((root(3)(2)x)^2+(root(3)(2)x)(5)+5^2)#

#color(white)(2x^3-125) = (root(3)(2)x-5)(root(3)(4)x^2+5root(3)(2)x+25)#

...noting that we have used

#(root(3)(2))^2 = root(3)(2^2) = root(3)(4)#