问题
计算题
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.
答案
解: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.