人教版七年级数学练习册上的一道有理数乘法题(2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005).
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![人教版七年级数学练习册上的一道有理数乘法题(2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005).](/uploads/image/z/654693-69-3.jpg?t=%E4%BA%BA%E6%95%99%E7%89%88%E4%B8%83%E5%B9%B4%E7%BA%A7%E6%95%B0%E5%AD%A6%E7%BB%83%E4%B9%A0%E5%86%8C%E4%B8%8A%E7%9A%84%E4%B8%80%E9%81%93%E6%9C%89%E7%90%86%E6%95%B0%E4%B9%98%E6%B3%95%E9%A2%98%EF%BC%882%2B1%2F2003%2B1%2F2004%2B1%2F2005%29%EF%BC%8A%EF%BC%881%2F2003%2B1%2F2004%2B1%2F2005%2B1%2F2006%EF%BC%89-%EF%BC%882%2B1%2F2003%2B1%2F2004%2B1%2F2005%2B1%2F2006%EF%BC%89%EF%BC%8A%281%2F2003%2B1%2F2004%2B1%2F2005%29.)
人教版七年级数学练习册上的一道有理数乘法题(2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005).
人教版七年级数学练习册上的一道有理数乘法题
(2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005).
人教版七年级数学练习册上的一道有理数乘法题(2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005).
令1/2003+1/2004+1/2005 =a
原式化为(2+a)*(a+1/2006)-(2+a+1/2006)*a
=2a+1/1003+a*a+1/2006*a-2a-a*a-1/2006*a
=1/1003
(2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005)
=2*(1/2003+1/2004+1/2005+1/2006)+(1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-...
全部展开
(2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005)
=2*(1/2003+1/2004+1/2005+1/2006)+(1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-2*(1/2003+1/2004+1/2005)-(1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005)
=2*【(1/2003+1/2004+1/2005+1/2006)-(1/2003+1/2004+1/2005)】+
【(1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005)】
=2*1/2006
=1/1003
收起
分解因式啊,设a=1/2003+1/2004+1/2005;
b=1/2003+1/2004+1/2005+1/2006;
则原式化为 (2+a)*b-(2+b)*a=2*b-2*a=2(b-a)=1/1003