化简[(xx-2xy+yy)(xx-2xy+yy)-xxxx+yyyy]÷(xx-yy)(xx-yy)的结果是

问题描述:

化简[(xx-2xy+yy)(xx-2xy+yy)-xxxx+yyyy]÷(xx-yy)(xx-yy)的结果是

第k项是C9(k-1)*(ax^2)^9-k+1)*(-1/x)^(k-1)
常数项则指数=0
20-2k-(k-1)=0
k=7
所以系数=C96*a^3=84
a=1
各项系数之和就是x=1的值
所以各项系数之和=(1-1/1)^9=0

原式=[(x-y)²(x-y)²-(x²+y²)(x²-y²)]/(x²-y²)²=[(x²-2xy+y²)-(x²+y²)]/(x²-y²)=-2xy/(x²-y²)