I'm asked to simplify
(x+2)^2 (x-1)^2 - (x-4)^2 (x+4)^2
something is wrong with this x^2 +4x +4 +x^2 - 1 -x^2 +16 +x^2 +8x +16
Since $\displaystyle a^2b^2 = (ab)^2$ it can be rewritten as $\displaystyle ((x+2)(x-1))^2 - ((x-4)(x+4))^2$
This gives an equation of the form $\displaystyle a^2-b^2$ so you can use the difference of two squares.
An alternative method is the one highlighted above
(x^2 +4x +4) (x^2 -2x -1) - (x^2 +16) (x^2 +8x +16)
-x^2 -16 (x^2 +8x +16)
-x^4 -8x^3 -16x^2 -16x^2 -128x -256
x^4 -2x^3 -x^2 + 4x^3 -8x -4x +4x^2 -8x -4 -x^2 - 16 -x^4 -8x^3 -16x^2 -16x^2 -128x -256
It's not finished yet I know. Once I started collecting like terms, I notice something was done wrong.