若代数式x^3+y^3+3x^2y+axy^2 含有因式x-y ,将这个代数式分解因式的结果是神马?

将x=y代入式子应为0,
即x^3+x^3+3x^3+ax^3=(a+5)x^3=0
所以a=-5
x^3+y^3+3x^2y-5xy^2=(x^3-y^3)+(2y^3-2xy^2)+(3x^2y-3xy^2)
=(x-y)(x^2+xy+y^2-2y^2+3xy)
=(x-y)(x^2+4xy-y^2)