x^4-2y^4-2x^3y-xy^3 因式分解- -.
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x^4-2y^4-2x^3y-xy^3 因式分解- -.
![x^4-2y^4-2x^3y-xy^3 因式分解- -.](/uploads/image/z/7099279-7-9.jpg?t=x%5E4-2y%5E4-2x%5E3y-xy%5E3+%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3-+-.)
x^4-2y^4-2x^3y-xy^3=x^4-y^4-y^4-x^3y-x^3y-xy^3=(x^2-y^2)(x^2+y^2)-(x^3+y^3)y-xy(x^2+y^2)=(x^2-y^2)(x^2+y^2)-(y+x)(x^2+y^2-xy)y-xy(x^2+y^2)=(x^2+y^2)(x^2-y^2-xy)-y(y+x)(x^2+y^2-xy)=(x^2+y^2)(x^2-xy)-y^2(x^2+y^2)-y(y+x)(x^2-xy)-y^3(x+y)=(x^2-xy)【x^2+y^2-y(y+x)】-y^2(x^2+y^2-xy-y^2)=(x^2-xy)(x^2-xy)-y^2(x^2-xy)=(x^2-xy-y^2)(x^2-xy)