`a)`

`5x^2(3x^2 - 1) - 6x(4x^3 - 3x + 1) - 2x^3(3x - 1)`

`= 15x^4 - 5x^2 - 24x^4 + 18x^2 - 6x - 6x^4 + 2x^3`

`= (15x^4 - 24x^4 - 6x^4) + 2x^3 + (-5x^2 + 18x^2) - 6x`

`= -15x^4 + 2x^3 + 13x^2 - 6x`

`b)`

`1/2x(x^2 - 2/5x + 2) - 3/4x^2(x + 1/3) - x(x + 1)`

`= 1/2x^3 - 1/5x^2 + x - 3/4x^3 - 1/4x^2 - x^2 - x`

`= (1/2x^3 - 3/4x^3) + (-1/5x^2 - 1/4x^2 - x^2) + (x - x)`

`= -1/4x^3 - 29/20x^2`

`c)`

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

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

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

`= -1/2x^4 - 5x^3 - 2`

`d)`

`x(x^3 - 2x^2) + 5x(x^2 - 2x + 1/2) - x^2(x^2 - x + 1)`

`= x^4 - 2x^3 + 5x^3 - 10x^2 + 5/2x - x^4 + x^3 - x^2`

`= (x^4 - x^4) + (-2x^3 + 5x^3 + x^3) + (-10x^2 - x^2) + 5/2x`

`= 4x^3 - 11x^2 + 5/2x`