在解题过程中,经常会遇到各项次数相同的式子(如x~2+xy+y~2),我们称它为齐次式.“齐次化”方法就是通过构造关系式,使非齐次式转化为齐次式,达到化繁为简、化难为易效果的一种数学方法,它是化归思想的具体体现.下面结合一些高考题与竞赛题分析运用“齐次化”方法解题的常见类型.1.巧妙代换,减少运算 In the process of solving problems, we often encounter the same number of the same number (such as x ~ 2 + xy + y ~ 2), we call it homogeneous. “Homogeneous” method is through the construction of relations Type, so that the non-homogeneous type into homogeneous type, to achieve complex and simple, easy to change the effect of a mathematical method, which is a concrete manifestation of the idea of ​​return to the following combination of some college entrance examination questions and competition analysis of the use of “ Homogeneous ”method to solve the common types of problems .1. Ingenious substitution, reduce computing