`a)` `(x-3)(5x-4)`

`= 5x^2 - 4x - 15x + 12`

`= 5x^2 -19x +12`

`b)` `(x-3)(-2x-4)`

`= -2x^2 -4x+6x+12`

`= -2x^2 +2x+12`

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

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

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

`d)` `(x+3)(x^2 + 3x-5)`

`= x^3 + 3x^2 - 5x + 3x^2 +9x -15`

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

`e)` `(x-5)(x^2-2x+3)`

`= x^3 -2x^2 + 3x - 5x^2 + 10x -15`

`= x^3 -7x^2 +13x -15`

`f)` `(x+2)(x-3)+x(x+1)`

`= x^2 -3x +2x -6 +x^2 +x`

`= 2x^2 -6`