完全平方公式是“整式乘除”一章的两个重要公式。除了直接用于计算两数和的平方、两数差的平方外,如果将它们适当变形,其用途更广、作用更大。现结合初一教学介绍完全平方公式的几个有用变形,供同志们教学中参考。 一、移项变形 (1)a~2+b~2=(a+b)~2-2ab; (2)a~2+b~2=(a-b)~2+2ab。 例1 设a、b、c、d都是整数,且 m=a~2+b~2,n=c~2+d~2,则mn也可以表示为两个整数的平方和。其形 The complete squared formula is the two important formulas in the “Multiplication, Division and Division” chapter. In addition to directly used to calculate the square of the sum of two numbers, the square of the difference between two numbers, if they are appropriately deformed, their use is wider and the effect is greater. Combined with the first-year teaching, several useful variants of the complete square formula are introduced for reference in comrades’ teaching. First, the transfer of deformation (1) a~2+b~2=(a+b)~2-2ab; (2)a~2+b~2=(a-b)~2+2ab. Example 1 Let a, b, c, and d be integers, and m=a~2+b~2,n=c~2+d~2, then mn can also be expressed as the sum of squares of two integers. Its shape