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.
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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