解x²-y²+x+y和x³-xy²+x+y

解x²-y²+x+y和x³-xy²+x+y
解x²-y²+x+y和x³-xy²+x+y

解x²-y²+x+y和x³-xy²+x+y
x²-y²+x+y
=（x+y）（x-y）+x+y
=(x+y)(x-y+1)
x³-xy²+x+y
=x(x²-y²)+x+y
=x(x+y)(x-y)+x+y
=(x+y)(x²-xy+1)
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x²-y²+x+y
=(x+y)(x-y)+(x+y)
=(x+y)(x-y+1)
x³-xy²+x+y
=x(x²-y²)+(x+y)
=x(x+y)(x-y)+(x+y)
=(x+y)[x(x-y)+1]
=(x+y)(x²-xy+1)