First, let's expand each expression:

For the first expression, we have (x-1)(x+1):

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

For the second expression, we have (x-2)(x^2+2x+4):

(x-2)(x^2+2x+4) = x(x^2 + 2x + 4) - 2(x^2 + 2x + 4) = x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 = x^3 - 8

Now we can subtract the two expressions:

x^2 - 1 - (x^3 - 8) = x^2 - 1 - x^3 + 8 = -x^3 + x^2 + 7

So, X(x-1)(x+1)-(x-2)(x^2+2x+4) simplifies to -x^3 + x^2 + 7.