# How do you factor #8u^3-24u^2v+18uv^2#?

##### 2 Answers

Feb 5, 2017

The answer is

#### Explanation:

We need

Therefore,

Feb 5, 2017

#### Explanation:

Given:

#8u^3-24u^2v+18uv^2#

Note that all of the terms are divisible by

Then the remaining quadratic is a perfect square trinomial, being of the form:

#A^2-2AB+B^2 = (A-B)^2#

with

#8u^3-24u^2v+18uv^2 = 2u(4u^2-12uv+9v^2)#

#color(white)(8u^3-24u^2v+18uv^2) = 2u((2u)^2-2(2u)(3v)+(3v)^2)#

#color(white)(8u^3-24u^2v+18uv^2) = 2u(2u-3v)^2#