（x^3 y^3)^2-4xy[x^4 x^2y^2 y^4-2xy(x^2-xy y^2)]

因式分解

热心网友

x^4+x^2*y^2+y^4=(x^4+2x^2y^2+y^4)-x^2y^2=(x^2+y^2)^2-(xy)^2=(x^2+y^2-xy)(x^2+y^2+xy)原式=(x^3+y^3)^2-4xy(x^2-xy+y^2)(x^2+xy+y^2-2xy)=(x+y)^2(x^2-xy+y^2)^2-4xy(x^2-xy+y^2)^2=(x^2-xy+y^2)^2*[(x+y)^2-4xy]=(x^2-xy+y^2)^2*(x^2-2xy+y^2)=(x-y)^2*(x^2-xy+y^2)^2

热心网友

（x^3+ y^3)^2-4xy[x^4 +x^2y^2 +y^4-2xy(x^2-xy +y^2)]==（x^3+ y^3)^2-4xy[(x^6 -y^6)/(x^2-y^2)-2xy(x^3+y^3)/(x+y)]==(x^3+x^3){(x^3+x^3)-4xy[(x^3 -y^3)/(x^2-y^2)-2xy/(x+y)]}==(x^2-xy +y^2)(x+y){(x^2-xy +y^2)(x+y)-4xy[(x^2+xy+y^2)/(x+y)-2xy/(x+y)]}==(x^2-xy +y^2)(x+y){(x^2-xy +y^2)(x+y)-4xy[(x^2-xy+y^2)/(x+y)]}==(x^2-xy +y^2)^2{(x+y)^2-4xy}=(x^2-xy +y^2)^2(x-y)^2.