提问(a^2-1)(a^2+1)(a-1)-(a^2-1)^2

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提问(a^2-1)(a^2+1)(a-1)-(a^2-1)^2

提问(a^2-1)(a^2+1)(a-1)-(a^2-1)^2
提问(a^2-1)(a^2+1)(a-1)-(a^2-1)^2

提问(a^2-1)(a^2+1)(a-1)-(a^2-1)^2
(a^2-1)(a^2+1)(a-1)-(a^2-1)^2
=(a^2-1)[(a^2+1)(a-1)-(a^2-1)]
=(a^2-1)(a^3-a^2+a-1-a^2+1)
=(a+1)(a-1)(a^3-2a^2+a)
=a(a+1)(a-1)(a^2-2a+1)
=a(a+1)(a-1)^3

a(a-1)^3(a+1)

(a^2-1)(a^2+1)(a-1)-(a^2-1)^2
=(a^2-1)[(a^2+1)(a-1)-(a^2-1)]
=(a^2-1)[(a^2+1)(a-1)-(a-1)(a+1)]
=(a+1)(a-1)(a-1)[(a^2+1)-(a+1)]
=(a+1)(a-1)(a-1)[a^2-a]
=a(a+1)(a-1)(a-1)(a-1)
=a(a+1)(a-1)^3

(a^2-1)(a^2+1)(a-1)-(a^2-1)^2
=(a+1)(a-1)(a^2+1)(a-1)-(a+1)^2(a-1)^2
=(a+1)(a-1)^2[(a^2+1)-(a+1)]
= (a+1)(a-1)^2(a^2-a)
=a(a+1)(a-1)^3