大师作文网x⁴2x⁴y+x⁴y²-2x²+y²-2x²
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/18 01:15:07
x⁴2x⁴y+x⁴y²-2x²+y²-2x²y²+2y+1
因式分解
因式分解
第二项少了一个符号,猜测应该是减号.
x⁴-2x⁴y+x⁴y²-2x²+y²-2x²y²+2y+1
= (x⁴-2x²+1)y²-2(x⁴-1)y+(1-2x²+x⁴)
= (x²-1)²y²-2(x²-1)(x²+1)y+(x²-1)²
= (x²-1)((x²-1)y²-2(x²+1)y+(x²-1))
= (x-1)(x+1)(x²(y²-2y+1)-(y²+2y+1))
= (x-1)(x+1)(x²(y-1)²-(y+1)²)
= (x-1)(x+1)(x(y-1)-(y+1))(x(y-1)+(y+1))
= (x-1)(x+1)(xy-x-y-1))(xy-x+y+1).
x⁴-2x⁴y+x⁴y²-2x²+y²-2x²y²+2y+1
= (x⁴-2x²+1)y²-2(x⁴-1)y+(1-2x²+x⁴)
= (x²-1)²y²-2(x²-1)(x²+1)y+(x²-1)²
= (x²-1)((x²-1)y²-2(x²+1)y+(x²-1))
= (x-1)(x+1)(x²(y²-2y+1)-(y²+2y+1))
= (x-1)(x+1)(x²(y-1)²-(y+1)²)
= (x-1)(x+1)(x(y-1)-(y+1))(x(y-1)+(y+1))
= (x-1)(x+1)(xy-x-y-1))(xy-x+y+1).
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