Đáp án:
$a)(x-1)\left(2x^2-9x+6\right)\\ b)(x-y)\left(-x^2 y - x^2 + 2 x y^2 + 2 x y - y^3\right)\\ c)(xy+2)(x-y)\\ d)(x-y)\left(x^2+2xy+2y^2\right)$
Giải thích các bước giải:
$a)2(x-1)^3-5(x-1)^2-(x-1)\\ =(x-1)\left(2(x-1)^2-5(x-1)-1\right)\\ =(x-1)\left(2(x^2-2x+1)-5x+5-1\right)\\ =(x-1)\left(2x^2-4x+2-5x+5-1\right)\\ =(x-1)\left(2x^2-9x+6\right)\\ b)y(y-x)^3-x(x-y)^2+xy(x-y)\\ =(x-y)\left(-y(x-y)^2-x(x-y)+xy\right)\\ =(x-y)\left(-y(x^2-2xy+y^2)-x^2+xy+xy\right)\\ =(x-y)\left(-x^2 y - x^2 + 2 x y^2 + 2 x y - y^3\right)\\ c)xy(x-y)-2y+2x\\ =xy(x-y)+2x-2y\\ =xy(x-y)+2(x-y)\\ =(xy+2)(x-y)\\ d)x(x+y)^2-y(x+y)^2+y^2(x-y)\\ =(x+y)^2(x-y)+y^2(x-y)\\ =(x-y)\left((x+y)^2+y^2\right)\\ =(x-y)\left(x^2+2xy+2y^2\right)$