1) (x+3)(x-1)-(x-7)(x-6)
<=> x2 –x+3x-3-(x2-6x-7x+42)
<=> x2-x+3x-3-x2+6x+7x-42
<=> 15x-45
<=> 15(x-3)
2) (-x-2)(x+1)-(x-5) (-x+1)
<=> (x+1) (-x-2-(x-5))
<=> (x+1) (-x-2-x+5)
<=> (x+1) (-2x+3)
3)5x(x-3)(x-1)-4x(x2-2x)
<=>5x(x-3)(x-1)-4x(x2-2x)
<=>5x (x2-x-3x+3)-4x3 + 8x2
<=>5x3- 5x2 -15x2 +15x -4x3+ 8x2
<=>x3-12x2+15x
<=>x(x2-12x+15)
4) -4x(x+3)(x-4)-3x(x^2-x+1)
<=>-4x(x+3)(x-4)-3x(x^2-x+1)
<=>-4x(x2-4x+3x-12)-3x3+4x2-3x
<=>-4x3+16x2-12x2+48x-3x3+4x2-3x
<=>-7x3+8x245x
5) 4x(x^2-x+3)-(x-6)(x-5)
<=>4x(x^2-x+3)-(x-6)(x-5)
<=>4x3-4x2+12x-(x2-5x-6x+30)
<=>4x3-4x2+12x-x2+5x+6x-30
<=>4x3-5x2+23x-30