`@Sun` 

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

`= 3x^3 - 5x^2 + 6x + 5 - x^3 + x^2 - 4x + 1` 

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

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

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

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

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

`= x^3 - 2x^2 - 3x - 2` 

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

`= (x^4 +3x+5) - (x^4 +x + 4x+1)` 

`= (x^4 +3x+5) - (x^4 + 5x+1)` 

`= x^4 + 3x + 5 - x^4 - 5x - 1` 

`= (x^4 - x^4) +(3x-5x) + (5-1)` 

`= -2x + 4` 

`4) (14x^3 + 2x^2 + 7x) - (11x^3 +x^2 +5x - 4)` 

`= 14x^3 + 2x^2 + 7x - 11x^3 - x^2 -5x + 4` 

`= (14x^3 -11x^3) + (2x^2 -x^2) +(7x -5x) + 4` 

`= 3x^3 + x^2 + 2x + 4` 

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

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

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

`= x^4 - x^3 - x^2 - 4x + 4` 

`6) (7x^3 + 3,5x^2 + 2x) - (5x^3 + 1,5x^2 + 5x -1)` 

`= 7x^3 + 3,5x^2 +2x - 5x^3 - 1,5x^2 - 5x + 1`

`= (7x^3 -5x^3) + (3,5x^2 - 1,5x^2) + (2x-5x) + 1`

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