观察:(1)14*16=224=1*(1+1)*100+4*6,(2)23*27=621=2*(2+1)*100+3*7,(3)32*38=1216=3*(3+1)*100+2*81.用公式(x+a)*(x+b)=x^2+(a+b)*x+ab证明上面所发现的规律.(提示:可设这两个两位数分别是(10n+a),(10n+b),其中a+b=10)2.简单叙
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 15:42:25
![观察:(1)14*16=224=1*(1+1)*100+4*6,(2)23*27=621=2*(2+1)*100+3*7,(3)32*38=1216=3*(3+1)*100+2*81.用公式(x+a)*(x+b)=x^2+(a+b)*x+ab证明上面所发现的规律.(提示:可设这两个两位数分别是(10n+a),(10n+b),其中a+b=10)2.简单叙](/uploads/image/z/8805363-51-3.jpg?t=%E8%A7%82%E5%AF%9F%3A%281%EF%BC%8914%2A16%3D224%3D1%2A%EF%BC%881%2B1%EF%BC%89%2A100%2B4%2A6%2C%282%2923%2A27%3D621%3D2%2A%282%2B1%29%2A100%2B3%2A7%2C%283%2932%2A38%3D1216%3D3%2A%283%2B1%29%2A100%2B2%2A81.%E7%94%A8%E5%85%AC%E5%BC%8F%28x%2Ba%29%2A%28x%2Bb%29%3Dx%5E2%2B%28a%2Bb%29%2Ax%2Bab%E8%AF%81%E6%98%8E%E4%B8%8A%E9%9D%A2%E6%89%80%E5%8F%91%E7%8E%B0%E7%9A%84%E8%A7%84%E5%BE%8B.%28%E6%8F%90%E7%A4%BA%3A%E5%8F%AF%E8%AE%BE%E8%BF%99%E4%B8%A4%E4%B8%AA%E4%B8%A4%E4%BD%8D%E6%95%B0%E5%88%86%E5%88%AB%E6%98%AF%2810n%2Ba%29%2C%2810n%2Bb%29%2C%E5%85%B6%E4%B8%ADa%2Bb%3D10%292.%E7%AE%80%E5%8D%95%E5%8F%99)
观察:(1)14*16=224=1*(1+1)*100+4*6,(2)23*27=621=2*(2+1)*100+3*7,(3)32*38=1216=3*(3+1)*100+2*81.用公式(x+a)*(x+b)=x^2+(a+b)*x+ab证明上面所发现的规律.(提示:可设这两个两位数分别是(10n+a),(10n+b),其中a+b=10)2.简单叙
观察:(1)14*16=224=1*(1+1)*100+4*6,(2)23*27=621=2*(2+1)*100+3*7,(3)32*38=1216=3*(3+1)*100+2*8
1.用公式(x+a)*(x+b)=x^2+(a+b)*x+ab证明上面所发现的规律.(提示:可设这两个两位数分别是(10n+a),(10n+b),其中a+b=10)
2.简单叙述以上所发现的规律
观察:(1)14*16=224=1*(1+1)*100+4*6,(2)23*27=621=2*(2+1)*100+3*7,(3)32*38=1216=3*(3+1)*100+2*81.用公式(x+a)*(x+b)=x^2+(a+b)*x+ab证明上面所发现的规律.(提示:可设这两个两位数分别是(10n+a),(10n+b),其中a+b=10)2.简单叙
可设这两个两位数分别是p=(10n+a),q=(10n+b),其中a+b=10
则有规律:p*q=(10n+a)(10n+b)=n*(n+1)*100+a*b
证明:
p*q=(10n+a)(10n+b)
=100n^2+(a+b)10n+ab
=10n(10n+a+b)+ab 注:a+b=10
=10n(10n+10)+ab
=100n(n+1)+ab
(10n+a)*(10n+b)=100n^2+10n(a+b)+ab=n(n+1)*100+a*b
(10n+a)*(10n+b)=10n*10n+(a+b)*10n+a*b=(10n+a+b)*10n+a*b=10*(n+1)*10n+a*b=n*(n+1)*100+a*b