#1
3a³b-12a²b+6ab=3ab(a²-4a+2)
x(x-1)+2(x-1)=(x-1)(x+2)
#2
xy+3y+xz+3z=(xy+xz)+(3y+3z)=x(y+z)+3(y+z)=(y+z)(x+3)
25-c²=(5-c)(5+c)
ab²-2abc+ac²=a(b²-2bc+c²)=a(b-c)²
#3
(x²-xy)/(x²-y²)=(x(x-y)/(x-y)(x+y)=x/(x+y)
#4
(a-2)(a+2)-a(a-1)=a²-4-a²+a=a-4
#5
(2x+8)²=0
2x+8=0
2x=-8|:2
x=-4
x²-4x=0
x(x-4)=0
x=0
или
x-4=0
x=4
#6
(a+b)(a-b)(a²+b²)=(a²-b²)(a²+b²)=a⁴+a²b²-b²a²-b⁴=a⁴b⁴
#7
c(c-2)(c+2)-(c+1)(c²-c+1)=c(c²-4)-(c³+1)=c³-4c-c³-1=-4c-1
#8
2x+2y-x²-2xy-y²=(-x²-y²)+(2x+2y-2xy)=
(2x+2y)+(-x²-2xy-y²)=2(x+y)-(x²+2xy+y²)=
2(x+y)-(x+y)²=(x+y)(2(-x-y)