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

1 Answer
Apr 3, 2017

Answer:

#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)#