Question

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

Answer 1

`4x(x-3)(x+1)`

Explanation:

There are 2 possible approaches to factorising this expression.

`color(blue)"Approach 1 " color(red)" Take out common factor"`

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

`color(red)(4x)[(x-1)^2-4]`

distribute bracket using FOIL and simplify.

`=4x(x^2-2x+1-4)`

`=4x(x^2-2x-3)larr" now factorise the quadratic"`

`[1xx-3=-3" and " 1-3=-2]`

`=4x(x-3)(x+1)`

`color(blue)"Approach 2 " color(red)" distribute and factorise"`

`rArr4x(x^2-2x+1)-16x`

`=4x^3-8x^2+4x-16x`

`=4x^3-8x^2-12x`

Take out `color(blue)"common factor "`of 4x

`=4x(x^2-2x-3)`

`=4x(x-3)(x+1)`