计算：（a1+a2+…+an-1)(a2+a3+…+an-1+an)-(a2+a3+…an-1)(a1+a2+…+an)

Question

计算：（a1+a2+…+an-1)(a2+a3+…+an-1+an)-(a2+a3+…an-1)(a1+a2+…+an)

Answer 1

令x=a2+a3+…an-1
则a1+a2+…+an-1=a1+x
a2+a3+…+an-1+an=x+an
a1+a2+…+an=a1+x+an
原式=(a1+x)(x+an)-x(a1+x+an)
=a1(x+an)+x(x+an)-x*a1-x(x+an)
=a1(x+an)-x*a1
=x*a1+a1a2-x*a1
=a1an