`a) (x - 3)(x + 5) - (x - 2)(x + 2)`

`= x^2 + 5x - 3x - 15 - (x^2 - 4)`

`= x^2 + 2x - 15 - x^2 + 4`

`= 2x - 11`

`b) (1/4x - y)(x^2 + 4xy + 16y^2) + 4(4y^3 - 1/16x^3 + 1)`

`= (1/4x)^3 - y^3 + 16y^3 - 1/4x^3 + 4`

`= 1/64x^3 - y^3 + 16y^3 - 1/4x^3 + 4`

`= (1/64x^3 - 16/64x^3) + (-y^3 + 16y^3) + 4`

`= -15/64x^3 + 15y^3 + 4`

`c) (x - 2)^2 + (x + 3)^2 - 2(x - 1)(x + 1)`

`= x^2 - 4x + 4 + x^2 + 6x + 9 - 2(x^2 - 1)`

`= 2x^2 + 2x + 13 - 2x^2 + 2`

`= 2x + 15`

`d) (x - 2)^2 + (x - 1)(x^2 + x + 1) - x(x - 2)(x + 2)`

`= x^2 - 4x + 4 + x^3 - 1 - x(x^2 - 4)`

`= x^3 + x^2 - 4x + 3 - x^3 + 4x`

`= x^2 + 3`