有这样一道题,计算:(x-y)[(x+y)2-xy]-(x-y)[(x-y)2+xy]-2xy(x-y)+3x2的值,其
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有这样一道题,计算:(x-y)[(x+y)2-xy]-(x-y)[(x-y)2+xy]-2xy(x-y)+3x2的值,其中x=2008,y=2009;某同学把“y=2009”错抄成“y=2090”但他的计算结果是正确的,请回答这是怎么回事?试说明理由.
![有这样一道题,计算:(x-y)[(x+y)2-xy]-(x-y)[(x-y)2+xy]-2xy(x-y)+3x2的值,其](/uploads/image/z/18760726-46-6.jpg?t=%E6%9C%89%E8%BF%99%E6%A0%B7%E4%B8%80%E9%81%93%E9%A2%98%EF%BC%8C%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%88x-y%EF%BC%89%5B%EF%BC%88x%2By%EF%BC%892-xy%5D-%EF%BC%88x-y%EF%BC%89%5B%EF%BC%88x-y%EF%BC%892%2Bxy%5D-2xy%EF%BC%88x-y%EF%BC%89%2B3x2%E7%9A%84%E5%80%BC%EF%BC%8C%E5%85%B6)
原式=(x-y)(x+y)2-xy(x-y)-(x-y)3-xy(x-y)-2xy(x-y)+3x2
=(x-y)(x+y)2-4xy(x-y)-(x-y)3+3x2
=(x-y)[(x+y)2-4xy-(x-y)2]+3x2
=3x2,
与y无关,所以y抄错不影响答案.
=(x-y)(x+y)2-4xy(x-y)-(x-y)3+3x2
=(x-y)[(x+y)2-4xy-(x-y)2]+3x2
=3x2,
与y无关,所以y抄错不影响答案.
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