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

1 Answer
George C.
Aug 29, 2016

(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]}

Related questions
See all questions in Factoring Completely
Impact of this question
3145 views around the world
You can reuse this answer
Creative Commons License