因式分解：(a-1)^2n-1+2(1-a)^2n+(a-1)^2n+1

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因式分解：(a-1)^2n-1+2(1-a)^2n+(a-1)^2n+1
因式分解：(a-1)^2n-1+2(1-a)^2n+(a-1)^2n+1

因式分解：(a-1)^2n-1+2(1-a)^2n+(a-1)^2n+1
原式=(a-1)^(2n-1)+2(1-a)^2n+(a-1)^(2n+1)
=(a-1)^(2n-1)+2(a-1)^2n+(a-1)^(2n+1)
=(a-1)^(2n-1)[1+2(a-1)+(a-1)^2]
=(a-1)^(2n-1)(1+a-1)^2
=(a-1)^(2n-1)a^2
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(x+y)^4(x-y)^2-(x+y)^2(y-x)^4
＝(x+y)^4(x-y)^2-(x+y)^2(x-y)^4
=(x+y)^2(x-y)^2[(x+y)^2-(x-y)^2]
=4xy(x+y)^2(x-y)^2
(a-1)^2n-1+2(1-a)^2n+(a-1)^2n+1
＝(a-1)^2n-1+2(a-1)^2n+(a-1)^2n+1

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(x+y)^4(x-y)^2-(x+y)^2(y-x)^4
＝(x+y)^4(x-y)^2-(x+y)^2(x-y)^4
=(x+y)^2(x-y)^2[(x+y)^2-(x-y)^2]
=4xy(x+y)^2(x-y)^2
(a-1)^2n-1+2(1-a)^2n+(a-1)^2n+1
＝(a-1)^2n-1+2(a-1)^2n+(a-1)^2n+1
=(a-1)^2n-1[1+2(a-1)+(a-1)^2]
=(a-1)^2n-1a^2
=a^2(a-1)^2n-1
4(x+y)^2+5-20(x+y-1)
=4(x+y)^2-20(x+y)+25
=[2(x+y)-5]^2
=(2x+2y-5)^2
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