\(a,2(x-1)^3-5(x-1)^2-(x-1)\\=(x-1)[2(x-1)^2-5(x-1)-1]\\=(x-1)[2(x^2-2x+1)-5x+5-1]\\=(x-1)(2x^2-4x+2-5x+4)\\=(x-1)(2x^2-9x+6)\\b,x(y-x)^3-y(x-y)^2+xy(x-y)\\=-x(x-y)^3-y(x-y)^2+xy(x-y)\\=(x-y)[-x(x-y)^2-y(x-y)+xy]\\=(x-y)[-x(x^2-2xy+y^2)-xy+y^2+xy]\\=(x-y)(-x^3+2x^2y-xy^2+y^2)\)
\(c,xy(x+y)-y(x+y)^2+y^2(x-y)\\=y[x(x+y)-(x+y)^2+y(x-y)]\\=y[x^2+xy-(x^2+2xy+y^2)+xy-y^2]\\=y(x^2+2xy-x^2-2xy-y^2-y^2)\\=y(-2y^2)\\=-2y^3\\d,x(x+y)^2-y(x+y)^2+xy-x^2\\=(x+y)^2(x-y)+x(y-x)\\=(x^2+2xy+y^2)(x-y)-x(x-y)\\=(x-y)(x^2+2xy+y^2-x)\\\text{#}Toru\)
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