(x-1)的四次方=ax的四次方+bx的三次方+cx的平方+dx+e

\u5df2\u77e5\uff08x+1)\u76845\u6b21\u65b9=ax\u76845\u6b21\u65b9+bx\u76844\u6b21\u65b9+cx\u76843\u6b21\u65b9+dx\u7684\u5e73\u65b9+ex+f,\u6c42\u4e0b\u5217\u5404\u5f0f\u7684\u503c

(x+1)^5 = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1

a = 1, b = 5, c = 10, d = 10, e = 5, f = 1,

a + b + c + d + e + f = (1+1)^5 = 32

b + c + d + e = 5 + 10 + 10 + 5 = 30

a + c + e = 1 + 10 + 1 = 12

(x-3)^5=Ax^5+Bx^4+Cx^3+Dx^2+Ex+F (1)
\u53d6x=1,\u4ee3\u4eba\u4e0a\u9762\u65b9\u7a0b\u4e2d\uff0c\u5f97\uff1a
\uff081-3\uff09^5=A+B+C+D+E+F
A+B+C+D+E+F=(1-3)^5=-32
\u53d6x=0,\u4ee3\u4eba\uff081\uff09\u5f97:
F=(0-3)^5=-243
\u53d6x=-1\u4ee3\u4eba\uff081\uff09\u5f97\uff1a
-A+B-C+D-E+F=\uff08-1-3\uff09^5=-1024
A-B+C-D+E=1024+F=1024-243=781

令x=1代入得
a+b+c+d+e=0

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