怎么用两种方法分解多项式xy(xy+4)-2(x+y)(x的2次-xy+y的2次)
如上,急
人气:417 ℃ 时间:2019-11-14 11:36:06
解答
第一种:xy(xy+4)-2(x+y)(x²-xy+y²)
=x²y²+4xy-2(x³-x²y+xy²+x²y-xy²+y³)
=x²y²+4xy-2x³-2y³
=(x²-2y)(-2x+y²)
第二种:
xy(xy+4)-2(x+y)(x²-xy+y²)
=x²y²+4xy-2(x+y)[(x+y)²-3xy]
=x²y²+4xy-2(x+y)³+6xy(x+y)
=x²y²+4xy-2(x³+3x²y+3xy²+y³)+6x²y+6xy²
=x²y²+4xy-2x³-2y³
=(x²-2y)(-2x+y²)
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