2) 5(x+2)(x-2) -1/2(6-8x)^2 +17
= 5(x^2-4) - 1/2(36-96x+64x^2) +17
= 5x^2 - 20 - 18 + 48x -32x^2 + 17
=  -27x^2 + 48x -21
3) (x+y)^2 - (x-y)^2 
= x^2 +2xy + y^2 - x^2 + 2xy - y^2
= 4xy 

4)  2.(x-y).(x+y) + (x+y)^2 + (x-y)^2
= (x+y+x-y)^2 = 4x^2

5)     (x-y+z)^2 + (z-y)^2  + 2(x-y+z) (y-z)
=  (x-y+z)^2 - 2(x-y+z) (z-y) + (z-y)^2
=  (x-y+z-z+y)^2
=  x^2

1/ (x+1)^2 - (x-1)^2 - 3(x+1)(x-1)
=(x+1-x+1)(x+1+x-1) - 3(x^2-1)
=4x-3x^2+3
=(3x-2-√13)(3x+√13-2)
2/5(x+2)(x-2) - 1/2(6-8x)^2 +17
=5(x^2-4) - 1/2(36-96x+64x^2) +17
=5x^2- 20 - 18 +48x -32x^2 +17
=48 - 27x^2 -21
=(x-1)(9x-7)
3/ (x+y)^2 + (x-1)^2 
=x^2 +2xy + y^2 + x^2 -2xy + y^2
=2(x^2+ y^2)
4/2(x-y)(x+y) + (x+y)^2 + (x-y)^2
=(x+y+x-y)^2
=4x^2
5/(x-y+z)^2 + (z-y)^2 + 2(x-y+z)(y-z)
=(x-y+z)^2 + (z-y)^2 - 2(x-y+z)(z-y)
= (x-y+z-z+y)^2
=x^2
6/ -3x(x+2)^2 + (x+3)(x-1)(x+1) - (2x-3)^2
= -3x(x^2 + 4x + 4) + (x+3)(x^2-1) - (4x^2 -12x + 9)
= -3x^3 -12x^2 -12x + x^3 - x +3x^2 - 3 - 4x^2 + 12x -9
=  -2x^3 -13x^2 - x -12
7/ (x-3)(x+3)(x+z) - (x-1)(x^2-3) - 5x (x+4)^2 - (x-5)^2
= (x^2 -9)(x+z) - x^3 +3x +x^2 -3 -5x^3- 40x^2 - 80x -x^2 +10x -25
= x^2z -9x - 9z - 5x^3 - 40x^2 - 67x - 28
=  -5x^3 + x^2(z-40) - 76x -9z - 28 

1/ (x+1)^2 - (x-1)^2 - 3(x+1)(x-1)
=(x+1-x+1)(x+1+x-1) - 3(x^2-1)
=4x-3x^2+3
=(3x-2-√13)(3x+√13-2)
2/5(x+2)(x-2) - 1/2(6-8x)^2 +17
=5(x^2-4) - 1/2(36-96x+64x^2) +17
=5x^2- 20 - 18 +48x -32x^2 +17
=48 - 27x^2 -21
=(x-1)(9x-7)
3/ (x+y)^2 + (x-1)^2 
=x^2 +2xy + y^2 + x^2 -2xy + y^2
=2(x^2+ y^2)
4/2(x-y)(x+y) + (x+y)^2 + (x-y)^2
=(x+y+x-y)^2
=4x^2
5/(x-y+z)^2 + (z-y)^2 + 2(x-y+z)(y-z)
=(x-y+z)^2 + (z-y)^2 - 2(x-y+z)(z-y)
= (x-y+z-z+y)^2
=x^2
6/ -3x(x+2)^2 + (x+3)(x-1)(x+1) - (2x-3)^2
= -3x(x^2 + 4x + 4) + (x+3)(x^2-1) - (4x^2 -12x + 9)
= -3x^3 -12x^2 -12x + x^3 - x +3x^2 - 3 - 4x^2 + 12x -9
=  -2x^3 -13x^2 - x -12
7/ (x-3)(x+3)(x+z) - (x-1)(x^2-3) - 5x (x+4)^2 - (x-5)^2
= (x^2 -9)(x+z) - x^3 +3x +x^2 -3 -5x^3- 40x^2 - 80x -x^2 +10x -25
= x^2z -9x - 9z - 5x^3 - 40x^2 - 67x - 28
=  -5x^3 + x^2(z-40) - 76x -9z - 28