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我们已学过乘法公式(a+b)(a-b)=a2-b2,如果把上式两边都加上b2,再交换位置,那么就得到a2=(a+b)·(a-b)+b2.应用这个变形后的公式可以进行一些简便运算.例1982=(98+2)(98-2)+22=100×96+4=9604.例29972=(997+3)(997-3)+32=1000×994+9=994009.例39892=(989-11)×1000+121=978121
We have learned that the multiplication formula (a+b)(ab)=a2-b2. If you add b2 to both sides of the equation and swap the positions, then you get a2=(a+b)(ab)+b2. Some simple calculations can be performed using this deformed formula. Example 1982=(98+2)(98-2)+22=100×96+4=9604. Example 29972=(997+3)(997-3)+ 32=1000×994+9=994009. Example 39892=(989-11)×1000+121=978121