(A1+A2+.An-1）（A2+A3+.+An-1+An)-(A2+A3+..An-1)(A1+A2+...An)计算

Question

(A1+A2+.An-1）（A2+A3+.+An-1+An)-(A2+A3+..An-1)(A1+A2+...An)
计算

Answer 1

令a=A1+A2+.An-1
则A2+A3+.+An-1+An=a-A1+An
A2+A3+..An-1=a-A1
A1+A2+...An=a+An
所以原式=a(a-A1+An)-(a-A1)(a+An)
=a(a-A1)+a*An-a(a-A1)-An(a-A1)
=a*An-a*An+A1*An
=A1*An