Calculate (x^2+1)-(x^2-4x+1)^2

Since it is a difference of squares, we'll apply the
formula:

a^2 - b^2 =
(a-b)(a+b)

We'll put a= x^2+1 and b =
x^2-4x+1

 (x^2+1)-(x^2-4x+1)^2 =
( x^2+1- x^2+4x-1)( x^2+1+x^2-4x+1)

We'll combine like
terms inside brackets:

(x^2+1)-(x^2-4x+1)^2 =
(4x)( 2x^2+2-4x)

(x^2+1)-(x^2-4x+1)^2 = 8x(x^2 - 2x +
1)

We notice that inside brackets we have a perfect
square:

(x^2+1)-(x^2-4x+1)^2 = 8x(x -
1)^2