因式分解：x的平方-xy-2y的平方+2x-y+1

题目

因式分解：x的平方-xy-2y的平方+2x-y+1

答案

x²-xy-2y²+2x-y+1=x²+2x+1-xy-y-2y²
=(x+1)²-y(x+1)-2y²
=(x+1)²-y²-y(x+1)-y²
=[(x+1)-y]*[(x+1)+y]-y[(x+1)+y]
=(x-y+1)(x+y+1)-y(x+y+1)
=(x+y+1)[(x-y+1)-y]
=(x+y+1)(x-2y+1)

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