Question : another basic rearrangement

Hi

How do you do this rearrangement:

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

but on the next line the book says its actually (1+x)(1-x)^2 (no  minus sign)

but either way i get -(1+x)(x-1)^2

thanks

Answer : another basic rearrangement

>> but when i factorised the equation i couldn't get (1-x)^2; i can only get (x-1)^2

If you can get (x-1)^2, then you can realize that :

        (x - 1)^2 = (x - 1) * (x - 1) = (x - 1) * (x - 1) * 1

Since -1 * -1 = 1 :

        (x - 1) * (x - 1) * 1 = (x - 1) * (x - 1) * -1 * -1 = ((x - 1) * -1) * ((x - 1) * -1) = (1 - x) * (1 - x) = (1 - x)^2


For any positive x :

        (-x)^2 = ((-1)^2) * (x^2) = 1 * x^2 = x^2