因式分解(a^2-a-1)(a^2-a-2)-20

设t=a²-a
(a^2-a-1)(a^2-a-2)-20
=(t-1)(t-2)-20
=t²-3t+2-20
=t²-3t-18
=(t-6)(t+3)
=(a²-a-6)(a²-a+3)
=(a-3)(a+2)(a²-a+3)

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令a^2-a = k
(a^2-a-1)(a^2-a-2)-20
= (k-1 ) (k-2) -20
= k ² -3k +2 -20
= k² -3k -18
= ( k-6) ( k+3)
= ( a^2-a -6) (a^2-a+3)
= (a-3) (a+2) (a^2-a+3)
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(a^2-a-1)(a^2-a-2)-20
=(a²-a)²-2(a²-a)-(a²-a)+2-20
=(a²-a)²-3(a²-a)-18
=(a²-a-6)(a²-a+3)
=(a+2)(a-3)(a²-a+3)