How do you factor 4x(x-1)^2 -16x?
1 Answer
Apr 3, 2017
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)
