Question

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

Answer 1

`(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]}