Разложите на множители, ответ, пожалуйста, пишите с решением(a-x)y^3-(a-y)x^3+(x-y)a^3

(a-x)y^3-(a-y)x^3+(x-y)a^3=ay³-xy³-ax³+x³y+(x-y)a^3=ay³-ax³+x³y-xy³+(x-y)a^3=a(y³-x³)+xy(х²-y²)+(x-y)a^3=-a(x³-y³)+xy(х²-y²)+(x-y)a^3=-a(x-y)(х²+ху+у²)+xy(х-y)(х+у)+(x-y)a^3= (x-y)(-a(х²+ху+у²)+xy(х+у)+a^3)=(x-y)(-aх²-аху-ау²+x²y+ху²+a^3)=(x-y)(-aх²+a^3+ху²-ау²+x²y-аху)= (x-y)(-a(х²-a²)+у²(х-а)+xy(х-а))=(x-y)(-a(х-a)(х+а)+у²(х-а)+xy(х-а))=(x-y)(х-a)(xy-aх-а²+у²)=(x-y)(х-a)(x(y-a)+(у+а)(у-а))=(x-y)(х-a)(y-a)(x+у+а)