\(1,x\left(x-1\right)+\left(1-x\right)^2\\ =\left(x-1\right)\left(x+x-1\right)\\ =\left(x-1\right)\left(2x-1\right)\\ 2,\left(x+1\right)^2-3\left(x+1\right)\\ =\left(x+1\right)\left(x+1-3\right)\\ =\left(x+1\right)\left(x-2\right)\\ 3,2x\left(x-2\right)-\left(x-2\right)^2\\ =\left(x-2\right)\left(2x-x+2\right)\\ =\left(x-2\right)\left(x+2\right)\)
\(4,3x\left(x-1\right)^2-\left(1-x\right)^3\\ =3x\left(x-1\right)^2+\left(x-1\right)^3\\ =\left(x-1\right)^2\left(3x+x-1\right)\\ =\left(x-1\right)^2\left(4x+1\right)\\ 5,3x\left(x+2\right)-5\left(x+2\right)^2\\ =\left(x+2\right)\left(3x-5x-10\right)\\ =\left(x+2\right)\left(-2x-10\right)=-2\left(x+2\right)\left(x+5\right)\\ 6,4x\left(x-y\right)+3\left(x-y\right)^2\\ =\left(x-y\right)\left(4x+3x-3y\right)\\ =\left(x-y\right)\left(7x-3y\right)\)
1: =x(x-1)+(x-1)^2
=(x-1)(x+x-1)
=(x-1)(2x-1)
2: (x+1)^2-3(x+1)
=(x+1)(x+1-3)
=(x+1)(x-2)
3: 2x(x-2)-(x-2)^2
=(x-2)(2x-x+2)
=(x-2)(x+2)
4: 3x(x-1)^2-(1-x)^3
=3x(x-1)^2+(x-1)^3
=(x-1)^2*(3x+x-1)
=(x-1)^2*(4x-1)
5: 3x(x+2)-5(x+2)^2
=(x+2)(3x-5x-10)
=(x+2)(-2x-10)
=-2(x+5)(x+2)
6: =4x(x-y)+3(x-y)^2
=(x-y)(4x+3x-3y)
=(x-y)(7x-3y)
