`a)`

`-2xy-(2x^3 y-3x^2 -y^2 + 7xy^3)`

`= -2xy - 2x^3 y + 3x^2 + y^2 - 7xy^3`

`b)`

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

`= -2x - x^3 + 3x^2 + x + 1`

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

`= -x - x^3 + 3x^2 + 1`

`c)`

`5y^2 . ( 2y^2 -y +8)`

`= (5y^2 . 2y^2) - (5y^2 . y) + (5y^2 . 8)`

`= 10y^4 - 5y^3 + 40y^2`

`d)`

`( -1/3 x^3 + 2/5 y -1/2 z) . ( -30xyz)`

`= [(-1/3 x^3) . (-30xyz)] - (2/5 y . 30xyz) + [(-1/2 z) . (-30xyz)]`

`= 10x^4 yz - 12 xy^2 z + 15xyz^2`

`e)`

`(5x-2y) .(x^2 -xy+1)`

`= (5x . x^2 - 5x . xy + 5x.1) - (2y.x^2 - 2y.xy + 2y.1)`

`= 5x^3 - 5x^2 y + 5x - 2x^2 y + 2xy^2 + 2y`

`= 5x^3 - (5x^2 y + 2x^2 y) +5x + 2xy^2 + 2y`

`= 5x^3 - 7x^2 y + 5x + 2xy^2 + 2y`

`g)`

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

`= 1/2 x^2 y^2 . (2x.2x - 2x.y + y.2x - y.y)`

`= 1/2 x^2 y^2 . (4x^2 - 2xy + 2xy - y^2)`

`= 1/2 x^2 y^2 . (4x^2 -y^2)`

`= (1/2 x^2 y^2 . 4x^2) - (1/2 x^2 y^2 . y^2)`

`= 2x^4 y^2 - 1/2 x^2 y^4`