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计算(a1+a2+...+an-1)x(a2+a3+...+an)-(a2+a3+...+an-1)(a1+a2+...+an)
题目详情
计算(a1+a2+...+an-1)x(a2+a3+...+an)-(a2+a3+...+an-1)(a1+a2+...+an)
▼优质解答
答案和解析
令x=A1+A2+.An-1
则A2+A3+.+An-1+An=x-A1+An
A2+A3+..An-1=x-A1
A1+A2+...An=x+An
所以原式=x(x-A1+An)-(x-A1)(x+An)
=x(x-A1)+x*An-x(x-A1)-An(x-A1)
=x*An-x*An+A1*An
=A1*An
则A2+A3+.+An-1+An=x-A1+An
A2+A3+..An-1=x-A1
A1+A2+...An=x+An
所以原式=x(x-A1+An)-(x-A1)(x+An)
=x(x-A1)+x*An-x(x-A1)-An(x-A1)
=x*An-x*An+A1*An
=A1*An
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