# How do you factor: y= 2x^3 -32x ?

##### 2 Answers
Apr 21, 2018

$y = 2 x \left(x + 4\right) \left(x - 4\right)$

#### Explanation:

$\left(1\right) \text{ }$we take out the $h c f s$

y=2x^3-32x

$h c f \left(2 , 32\right) = 2$

$y = \textcolor{red}{2} \left({x}^{3} - 16 x\right)$

$h c f \left(x , {x}^{3}\right) = x$

$y = 2 \textcolor{red}{x} \left({x}^{2} - 16\right)$

$\left(2\right) \text{ }$apply difference of squares

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

$y = 2 x \left(x + 4\right) \left(x - 4\right)$

Apr 21, 2018

$y = 2 x \left(x - 4\right) \left(x + 4\right)$

#### Explanation:

$\text{take out a "color(blue)"common factor } 2 x$

$= 2 x \left({x}^{2} - 16\right)$

${x}^{2} - 16 \text{ is a "color(blue)"difference of squares}$

$\text{which factors in general as}$

â€¢color(white)(x)a^2-b^2=(a-b)(a+b)#

$\text{here "a=x" and } b = 4$

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

$\Rightarrow y = 2 x \left(x - 4\right) \left(x + 4\right)$