X的6次方-Y的6次方-2X的3次方+1X的平方（X+1）-Y（XY+X）

Question

X的6次方-Y的6次方-2X的3次方+1
X的平方（X+1）-Y（XY+X）

Answer 1

x^6-y^6-2x^3+1
=(x^6-2x^3+1)-y^6
=(x^3-1)^2-(y^3)^2
=(x^3+y^3-1)(x^3-y^3-1)
x^2(x+1)-y(xy+x)
=x^3+x^2-xy^2-xy
=(x^3-xy^2)+(x^2-xy)
=x(x^2-y^2)+x(x-y)
=x(x+y)(x-y)+x(x-y)
=(x-y)(x^2+xy+x)