观察例题按规律回答问题(120×120)-(119×121)=1(120×120)-(118×122)=4(120×120)-(117×123)=9(120×120)-(116×124)=16问:(120×120)-(112×128)=( )(120×120)-( × )=( )要
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![观察例题按规律回答问题(120×120)-(119×121)=1(120×120)-(118×122)=4(120×120)-(117×123)=9(120×120)-(116×124)=16问:(120×120)-(112×128)=( )(120×120)-( × )=( )要](/uploads/image/z/8493060-12-0.jpg?t=%E8%A7%82%E5%AF%9F%E4%BE%8B%E9%A2%98%E6%8C%89%E8%A7%84%E5%BE%8B%E5%9B%9E%E7%AD%94%E9%97%AE%E9%A2%98%EF%BC%88120%C3%97120%EF%BC%89-%EF%BC%88119%C3%97121%EF%BC%89%EF%BC%9D1%EF%BC%88120%C3%97120%EF%BC%89-%EF%BC%88118%C3%97122%EF%BC%89%EF%BC%9D4%EF%BC%88120%C3%97120%EF%BC%89-%EF%BC%88117%C3%97123%EF%BC%89%EF%BC%9D9%EF%BC%88120%C3%97120%EF%BC%89-%EF%BC%88116%C3%97124%EF%BC%89%EF%BC%9D16%E9%97%AE%EF%BC%9A%EF%BC%88120%C3%97120%EF%BC%89-%EF%BC%88112%C3%97128%EF%BC%89%EF%BC%9D%EF%BC%88+%EF%BC%89%EF%BC%88120%C3%97120%EF%BC%89-%EF%BC%88+%C3%97+%EF%BC%89%EF%BC%9D%EF%BC%88+%EF%BC%89%E8%A6%81)
观察例题按规律回答问题(120×120)-(119×121)=1(120×120)-(118×122)=4(120×120)-(117×123)=9(120×120)-(116×124)=16问:(120×120)-(112×128)=( )(120×120)-( × )=( )要
观察例题按规律回答问题
(120×120)-(119×121)=1
(120×120)-(118×122)=4
(120×120)-(117×123)=9
(120×120)-(116×124)=16
问:
(120×120)-(112×128)=( )
(120×120)-( × )=( )
要解题思路
同志们,
观察例题按规律回答问题(120×120)-(119×121)=1(120×120)-(118×122)=4(120×120)-(117×123)=9(120×120)-(116×124)=16问:(120×120)-(112×128)=( )(120×120)-( × )=( )要
由前面的几个式子我们看得出被减数是 120×120
减数第1项是 (120-1)×(120+1),(120-2)×(120+2),(120-3)×(120+3),那么第x个式子就能表示成 (120×120)-(120-x)(120+x)
再看差,第1个是1的平方,第二个是2的平方,第三个是3的平方.那么第x个式子的差就是x的平方,即 x^2
112 = 120 - 8,所以是第八个式子,差就是8的平方,64
最后一个式子就是刚地解释的 (120×120)-(120-x)×(120+x) = x^2
(120×120)-(112×128)=(64)
(120×120)-(111×129)=(81)
119*121=(120-1)*(120+1)=(120*120)-1*1
118*122=(120-2)*(120+2)=(120*120)-2*2
依次类推:(120×120)-(112×128)
=(120×120)-(120*120)+8*8=64