We need to find (x^2 + 1) - (x^2 - 4x + 1)^2

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

=> x^2 + 1 - [(x^2 - 4x) + 1]^2

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

=> x^2 + 1 - x^4 - 16x^2 + 8x^3 - 1 - 2x^2 + 8x

=> -x^4 + 8x^3 -17x^2 + 8x

**The required value is -x^4 + 8x^3 -17x^2 + 8x**