x³-x ²y-xy ²+y³怎么因式分解

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x³-x ²y-xy ²+y³怎么因式分解
x³-x ²y-xy ²+y³怎么因式分解

x³-x ²y-xy ²+y³怎么因式分解
x2(x-y)-y2(x-y)
(x2-y2)(x-y)
(x-y)2(x+y)

x2(x-y)-y2(x-y)=(x2-y2)(x-y)=(x+y)(x-y)2

=(x3+y3)-(x2y+xy2)
=(x+y)(x2-xy+y2)-xy(x+y)
=(x+y)(x2-xy+y2-xy)
=(x+y)(x2-2xy+y2)
=(x+y)(x-y)2

x³-x ²y-xy ²+y³=x ²(x-y)+y ²(y-x)=(x-y)(x ²-y ²)=(x+y)(x-y)²