(1+x+x²)(1-x+x²)(1-x²+x四次)(1-x四次+x八次)简便算

(1+x+x²)(1-x+x²)(1-x²+x四次)(1-x四次+x八次)简便算
(1+x+x²)(1-x+x²)(1-x²+x四次)(1-x四次+x八次)简便算

(1+x+x²)(1-x+x²)(1-x²+x四次)(1-x四次+x八次)简便算

(1+x+x²)(1-x+x²)
=(1+x²+x)(1+x²-x)
=(1+x²)^2-x^2
=1+x四次+x²
(1+x+x²)(1-x+x²)(1-x²+x四次)
=(1+x四次+x²)(1+x四次-x²)
=(1+x四次)^2-x^...

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(1+x+x²)(1-x+x²)
=(1+x²+x)(1+x²-x)
=(1+x²)^2-x^2
=1+x四次+x²
(1+x+x²)(1-x+x²)(1-x²+x四次)
=(1+x四次+x²)(1+x四次-x²)
=(1+x四次)^2-x^4
=1+x四次+x八次
(1+x+x²)(1-x+x²)(1-x²+x四次)(1-x四次+x八次)
=(1+x四次+x八次）(1-x四次+x八次)
=1+x四次+x八次+x十六次
这里主要是用到平方差的公式
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