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因式分解的应用几乎无处不在,现精选几例与你分享.一、数字计算例1计算:203~2+203×194+97~2.解析:因为算式中的203×194=2×203×97,而算式两端分别是203~2和97~2,对照平方和公式的结构特点,知此数字计算题可利用平方和公式分解因式求解:原式=203~2+2×203×97+97~2=(203+97)~2=300~2=90000.评注:这类数字计算题,如果按常规方法顺序演算,计算量大且易出错.利用因式分解的方法,则可简化运算过程,提高计算的准确度.
The application of factorization is almost ubiquitous, now select a few to share with you. First, the calculation of a numerical example 1: 203 ~ 2 +203 × 194 +97 ~ 2. Analysis: Because the formula 203 × 194 = 2 × 203 × 97, and the two ends of the formula are 203 ~ 2 and 97 ~ 2, the structure of the square and the formula of the structural characteristics of this number can be calculated using the square sum formula decomposition factoring solution: the original = 203 ~ 2 +2 × 203 × 97 + 97 ~ 2 = (203 + 97) ~ 2 = 300 ~ 2 = 90000. Comment: This type of digital calculation problems, if calculated according to the conventional method, the calculation is large and error-prone. Method, you can simplify the calculation process, improve the accuracy of the calculation.