f.2 math factorization of simple polynomials

1. (x+y)^2 -(2x-y)^2
= (x+y +2x-y)(x+y-2x-y)
= 3x(-x)
= -3x^2
2. (a-2)^3-1
= (a-2-1)[(a-2)^2+(a-2)+1]
= (a-3)(a^2 -4a+4+a-1)
= (a-3)(a^2 -3a +3)
3. -x^4+27x
= x(27- x^3)
= x(3-x)(9+3x+x^2)
4. a^3+b^3-2a^2b-2ab^2
= (a+b)(a^2-ab+b^2) -2ab(a+b)
= (a+b)(a^2-ab+b^2-2ab)
= (a+b)(a^2-3ab+b^2)
5. 2(15m^2-21)+m
= 30m^2 +m -42
= (6m -7)(5m+6)
6. 10r^3s+18r^2s^2-36rs^3
= 2rs(5r^2 + 9rs - 18s^2)
= 2rs(5r- 6s)(r+3s)
7.(x-2)^2-9/2x^2-x-3 (6-4x)
= (x^2-4x+4-9)/(x+1)(2x-3) (6-4x)
= (x^2-4x-5)/(x+1)(2x-3) 2(3-2x)
= (x+1)(x-5)/(x+1)(2x-3) 2(3-2x)
= (x-5)/(2x-3) 2(3-2x)
= 2(5-x)
8. 20x^2+11xy-3y^2
= (5x - y)(4x + 3y)
9. 20(x+3y)^2+11(x+3y)(2x+1)-3(2x+1)^2
= [5(x+3y) - (2x+1)][4(x+3y) + 3(2x+1)]
= (3x+15y-1)(10x+12y+3)
10.(2x/x-2 - 4/x-3) x-3/x-4
= [2x(x-3)-4(x-2)]/(x-2)(x-3) (x-3)/(x-4)
= (2x^2 -6x -4x +8)/(x-2)(x-3) (x-3)/(x-4)
= (2x^2 -10x +8)/(x-2)(x-3) (x-3)/(x-4)
= 2(x-4)(x-1)/(x-2)(x-3) (x-3)/(x-4)
= 2(x-1)/(x-2)