因式分解x²+x-y²+y

因式分解x²+x-y²+y
因式分解x²+x-y²+y

因式分解x²+x-y²+y
原式
=(x+y)+(x²-y²)——分组分解
=(x+y)+(x+y)(x-y)——平方差
=(x-y+1)(x+y)——合并
这种题目要善于观察,

=x²-y²+x+y
=(x+y)(x-y)+(x+y)
=(x+y)(x-y+1)

(x+y)(x-y+1)

x2-x-y2-y 解法：=(x2-y2)-(x+y) =(x+y)(x-y)-(x+y) =(x+y)(x-y-1) 求采纳

原式=(x²-y²)+(x+y)
=(x+y)(x-y)+(x+y)
=(x+y)(x-y+1)