x²y²-x²-y²+1 x²-2x-4y²-4y

来源：学生作业帮助网编辑：作业帮时间：2024/05/15 17:09:13

x²y²-x²-y²+1 x²-2x-4y²-4y
x²y²-x²-y²+1 x²-2x-4y²-4y

x²y²-x²-y²+1 x²-2x-4y²-4y
x²y²-x²-y²+1
=x²(y²-1)-(y²-1)
=(x²-1)(y²-1)
=(x+1)(x-1)(y+1)(y-1)
x²-2x-4y²-4y
=x²-2x+1- (4y²+4y+1)
=(x-1)²-(2y+1)²
= [(x-1)+(2y+1)]*[(x-1)-(2y+1)]
=(x+2y)(x-2y-2)

x²y²-x²-y²+1
=(x²y-x²)-(y²-1)
=x²(y²-1)-(y²-1)
=(y²-1)(x²-1)
=(y+1)(y-1)(x+1)(x-1)

x²-2x-4y²-4y
=x²-4y²-2x-4y
=(x+2y)(x-2y)-2(x+2y)
=(x+2y)(x-2y-2)

x²y²-x²-y²+1=(1-x²)(1-y²)
x²-2x-4y²-4y=(x-1)²-(2y+1)²=(x-2y-2)(x+2y)