化简: (a1+a2+……+an-1)•(a2+a3+……+an-1+an) -(a2+a3+……+an-1)•(a1+a2+……+an)
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化简: (a1+a2+……+an-1)•(a2+a3+……+an-1+an) -(a2+a3+……+an-1)•(a1+a2+……+an)
化简: (a1+a2+……+an-1)•(a2+a3+……+an-1+an) -(a2+a3+……+an-1)•(a1+a2+……+an)
化简: (a1+a2+……+an-1)•(a2+a3+……+an-1+an) -(a2+a3+……+an-1)•(a1+a2+……+an)
分析:本题可先设a2+a3+a4+…+an-1=x,将原式进行化简后求解.
设a2+a3+a4+…+an-1=x.
原式=(a1+x)(x+an)-x(a1+x+an),
=x2+a1x+anx+a1an-a1x-x2-xan,
=a1an.
故本题答案为:a1an.
(a1+a2+……+an-1)•(a2+a3+……+an-1+an) -(a2+a3+……+an-1)•(a1+a2+……+an)
= (a1+a2+……+an-1)•(a2+a3+……+an-1)+(a1+a2+……+an-1)•(an) -(a2+a3+……+an-1)•(a1+a2+……)-(a2+a3+……+an-1)...
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(a1+a2+……+an-1)•(a2+a3+……+an-1+an) -(a2+a3+……+an-1)•(a1+a2+……+an)
= (a1+a2+……+an-1)•(a2+a3+……+an-1)+(a1+a2+……+an-1)•(an) -(a2+a3+……+an-1)•(a1+a2+……)-(a2+a3+……+an-1)•(an)
=(a1+a2+……+an-1)•(an) -(a2+a3+……+an-1)•(an)
=a1•an
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