(1+x+x²)(1-x+x²)(1-x²+x四次)(1-x四次+x八次)简便算
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![(1+x+x²)(1-x+x²)(1-x²+x四次)(1-x四次+x八次)简便算](/uploads/image/z/1095790-22-0.jpg?t=%281%2Bx%2Bx%26%23178%3B%29%281-x%2Bx%26%23178%3B%29%281-x%26%23178%3B%2Bx%E5%9B%9B%E6%AC%A1%29%281-x%E5%9B%9B%E6%AC%A1%2Bx%E5%85%AB%E6%AC%A1%29%E7%AE%80%E4%BE%BF%E7%AE%97)
(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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