Question

计算（a1+a2+...+an-1)x(a2+a3+...+an)-(a2+a3+...+an-1)(a1+a2+...+an) 请各位高手指教、、、

Answer 1

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

Answer 2

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

Answer 3

• 
  

  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