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

1 Answer
Aug 29, 2016

Answer:

#(x^2-1)^2-(x-1)^2=(x-1)^2x(x+2)#

Explanation:

Note that #x^2-1 = x^2-1^2 = (x-1)(x+1)#

So we find:

#(x^2-1)^2-(x-1)^2#

#=(x-1)^2(x+1)^2-(x-1)^2#

#=(x-1)^2((x+1)^2-1)#

#=(x-1)^2(x^2+2x+color(red)(cancel(color(black)(1)))-color(red)(cancel(color(black)(1))))#

#=(x-1)^2x(x+2)#

graph{(x^2-1)^2-(x-1)^2 [-10, 10, -5.5, 4.5]}