论文部分内容阅读
有理数平方的计算,在中学数学的学习和生产实践中,都经常用到。关于这个问题,现行初中《数学》课本第二册里,在讲到“两数和的平方公式”时,介绍了个别特殊数的平方幂的简便算法,但这些方法的局限性很大,应用不广。本文仍用这个公式作为理论基础,介绍一个普遍适用的“分段捷乘法”。先看两位数的情况。因为两位数能表示为10a+b的形式,按完全平方公式有: (10a+b)~2=(10a)~2+2·10ab+b~2=(10a+2b)10a+b~2 (Ⅰ)把恒等式(Ⅰ)写为竖式有:按右边这个用逗号代替乘式与波乘式间的加号后
The calculation of rational squares is often used in the learning and production practices of middle school mathematics. Regarding this issue, in the second volume of the textbook “Mathematics” in the current junior middle school, when the “square formula of two-number sums” is mentioned, a simple algorithm for the square power of individual special numbers is introduced. However, these methods have great limitations. Not wide. This article still uses this formula as a theoretical basis to introduce a universally applicable “segmented multiplication method.” Look at the double-digit situation first. Because the two-digit number can be expressed in the form of 10a+b, according to the complete square formula: (10a+b)~2=(10a)~2+2•10ab+b~2=(10a+2b)10a+b~ 2 (I) Write the identity (I) as vertical: press comma in place of the plus sign between the multiplication and wave multiplication