因式分解：x^4+2(x^3)*y-3(x^2)(y^2)-4x(y^3)-y^4_数学解答

因式分解：x^4+2(x^3)*y-3(x^2)(y^2)-4x(y^3)-y^4

人气：442 ℃　时间：2020-03-22 10:21:48

解答

x^4+2x^3y+x^2y^2-(4x^2y^2+4xy^3+y^4)=x^2(x+y)^2-y^2(2x+y)^2=(x^2+xy+2xy+y^2)(x^2+xy-2xy-y^2)
=(x^2+3xy+y^2)(x^2-xy-y^2)