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(3)(a+b)2是宝库从上一节已经知道:八个乘法公式中有6个是可以从(a十b)2直接或间接地导出的,由此可见公式(a+b)2=a2+2ab+b2的不平凡.这一节你将看到由这个公式可生长出很多有趣又有用的东西,它们让你惊奇,…在公式(a+b)2=a2+2ab+b2中,让a表示自然数n,让b表示1,它就变成 (n+1)2=n2+2n+1. 这是一个恒等式.当n取某一个具体的自然数时,它就变成一个具体的数字等式.例如当n取99时,就得到
(3)(a+b)2 is a treasure trove As already known from the previous section, six of the eight multiplication formulae can be derived directly or indirectly from (a, b, b)2, from which the formula (a+b) can be seen. ) 2=a2+2ab+b2 is not trivial. In this section you will see that this formula can grow a lot of interesting and useful things, they make you wonder, ... in formula (a+b)2=a2+2ab In +b2, letting a represent the natural number n and let b represent 1, it becomes (n+1)2=n2+2n+1. This is an identity. When n takes a specific natural number, it changes Into a concrete numerical equation. For example, when n takes 99,