# How do you factor 4x(x-1)^2 -16x?

Apr 3, 2017

$4 x \left(x - 3\right) \left(x + 1\right)$

#### Explanation:

There are 2 possible approaches to factorising this expression.

$\textcolor{b l u e}{\text{Approach 1 " color(red)" Take out common factor}}$

Note there is a common factor of 4x in both terms which can be taken out.

$\textcolor{red}{4 x} \left[{\left(x - 1\right)}^{2} - 4\right]$

distribute bracket using FOIL and simplify.

$= 4 x \left({x}^{2} - 2 x + 1 - 4\right)$

$= 4 x \left({x}^{2} - 2 x - 3\right) \leftarrow \text{ now factorise the quadratic}$

$\left[1 \times - 3 = - 3 \text{ and } 1 - 3 = - 2\right]$

$= 4 x \left(x - 3\right) \left(x + 1\right)$

$\textcolor{b l u e}{\text{Approach 2 " color(red)" distribute and factorise}}$

$\Rightarrow 4 x \left({x}^{2} - 2 x + 1\right) - 16 x$

$= 4 {x}^{3} - 8 {x}^{2} + 4 x - 16 x$

$= 4 {x}^{3} - 8 {x}^{2} - 12 x$

Take out $\textcolor{b l u e}{\text{common factor }}$of 4x

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

$= 4 x \left(x - 3\right) \left(x + 1\right)$