转化是中学数学解题的基本思想。在含有多个变元的问题中,可以选取某个变元做为主要变元,不妨称之为主元。将问题转化为关于该主元的式子、方程或函数,使问题获得巧解。这种转化的方法,称为主元法。下面举例说明这种方法在解题中的应用。 一、分解因式 例1 分解因式: (1+y)~2-2x~2(1+y~2)+x~4(1-y)~2。 (1986年江苏省扬州市初一数学竞赛试题) Transformation is the basic idea of ​​solving problems in middle school mathematics. In a problem with multiple variables, one of the variables can be selected as the main variable, which may be called the pivot element. Translate the question into an equation, equation, or function about that pivot element to get the problem solved. This method of transformation is called the principal element method. The following example illustrates the application of this method in problem solving. First, the factorization factor of decomposition factor 1 is: (1+y)~2-2x~2(1+y~2)+x~4(1-y)~2. (1986 Yangzhou City, Jiangsu Province, the first math contest test questions)