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

问题描述:

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