找规律并证明:15*15=1*2*100+25=225,25*25=2*3*100+25=625

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 03:13:17
找规律并证明:15*15=1*2*100+25=225,25*25=2*3*100+25=625

找规律并证明:15*15=1*2*100+25=225,25*25=2*3*100+25=625
找规律并证明:15*15=1*2*100+25=225,25*25=2*3*100+25=625

找规律并证明:15*15=1*2*100+25=225,25*25=2*3*100+25=625
即(10n+5)*(10n+5)=n*(n+1)*100+25
证明
(10n+5)*(10n+5)
=10n(10n+5)+5(10n+5)
=100n²+50n+50n+25
=100n²+100n+25
=n*(n+1)*100+25