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数学中有很多命题是通过对某些特殊情形的抽象、概括而得到的。解题时,如果能注意到从命题的特殊情形入手进行由此及彼的联想,往往可使复杂问题简单化,抽象问题具体化。下而就特殊性在解题中的作用举例说明之。一、利用特殊简化计算例1.计算多项式(5x~5-x~4-3x-2)~(100)·(10x-9)~2·(9x~3-7x-2)~(78)展开式的系数和。解这个多项式的展开式的最高次数为 5×100+1×2+3×78=736, 所以原多项式可表达为 (5x~5-x~4-3x-2)~(100)·(10x-9)~2·(9x~3-7x-2)~(78)=a,x~(736)+a_2x~(735)+…+a_(736)x+a_(737), 其中a_i(i=1,2,…,737)为x各项相应的系数。令x=1,得原多项式展开式系数和
There are many propositions in mathematics that are obtained through the abstraction and generalization of certain special situations. When solving a problem, if you can notice that the special situations of the propositions start with the association of others, you can often make complex problems simple and abstract problems concrete. Let’s take an example of the role of particularity in solving problems. First, using a special simplified calculation example 1. Calculate the polynomial (5x~5-x~4-3x-2)~(100)(10x-9)~2(9x~3-7x-2)~(78) Expansion coefficient and. The maximum number of times to solve this polynomial expansion is 5 × 100 + 1 × 2 + 3 × 78 = 736, so the original polynomial can be expressed as (5x~5-x ~ 4-3x-2) ~ (100) · (10x -9)~2(9x~3-7x-2)~(78)=a,x~(736)+a_2x~(735)+...+a_(736)x+a_(737), where a_i( i=1, 2, ..., 737) are the corresponding coefficients for x. Let x=1, get the original polynomial expansion coefficient and