Question

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

Answer 1

`y=2x(x+4)(x-4)`

Explanation:

`(1)" "`we take out the `hcfs`

y=2x^3-32x#

`hcf(2,32)=2`

`y=color(red)(2)(x^3-16x)`

`hcf(x,x^3)=x`

`y=2color(red)(x)(x^2-16)`

`(2)" "`apply difference of squares

`a^2-b^2=(a+b)(a-b)`

`y=2x(x+4)(x-4)`

Answer 2

`y=2x(x-4)(x+4)`

Explanation:

`"take out a "color(blue)"common factor "2x`

`=2x(x^2-16)`

`x^2-16" is a "color(blue)"difference of squares"`

`"which factors in general as"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"here "a=x" and "b=4`

`rArrx^2-16=(x-4)(x+4)`

`rArry=2x(x-4)(x+4)`