因式分解:x3+x2-y3-y2=

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因式分解:x3+x2-y3-y2=
因式分解:x3+x2-y3-y2=

因式分解:x3+x2-y3-y2=
x3+x2-y3-y2
=x3-y3+x2-y2
=(x-y)(x2+xy+y2)+(x-y)(x+y)
=(x-y)(x+y+x2+xy+y2)


原式
=x³-y³+x²-y²
=(x-y)(x²+xy+y²)+(x+y)(x-y)
=(x-y)(x²+xy+y²+x+y)

x3-y3=(x-y)(x2+xy+y2)
x2-y2=(x-y)(x+y)
因此,原式=(x-y)(x2+xy+y2+x+y)

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