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多项式相除问题(x6+x5y–xy5–y6):(x4+x3y+x2y2+xy3+y4)
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答案和解析
(x6 + x5y – xy5 – y6):(x4 + x3y + x2y2 + xy3 + y4)
=[(x6 – y6)+xy(x4– y4 )]/ (x4 + x3y + x2y2 + xy3 + y4)
=[(x2-y2)(x4+x2y2+y4)+xy(x2+y2)(x2-y2)]/(x4 + x3y + x2y2 + xy3 + y4)
=(x2-y2)(x4+x2y2+y4+x3y+xy3)/(x4 + x3y + x2y2 + xy3 + y4)
=x2-y2
=[(x6 – y6)+xy(x4– y4 )]/ (x4 + x3y + x2y2 + xy3 + y4)
=[(x2-y2)(x4+x2y2+y4)+xy(x2+y2)(x2-y2)]/(x4 + x3y + x2y2 + xy3 + y4)
=(x2-y2)(x4+x2y2+y4+x3y+xy3)/(x4 + x3y + x2y2 + xy3 + y4)
=x2-y2
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