(a-1)(a-2)(a-3)(a-4)-3因式分解,

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(a-1)(a-2)(a-3)(a-4)-3因式分解,

(a-1)(a-2)(a-3)(a-4)-3因式分解,
(a-1)(a-2)(a-3)(a-4)-3因式分解,

(a-1)(a-2)(a-3)(a-4)-3因式分解,
(a-1)(a-2)(a-3)(a-4)-3=(a²-5a+4)(a²-5a+6)-3
=(a²-5a)²+10(a²-5a)+24-3
=(a²-5a)²+10(a²-5a)+21
=(a²-5a+3)(a²-5a+7)

原式=[(a-1)(a-4)]×[(a-2)(a-3)]-3=(a²-5a+4)(a²-5a+6)-3=[(a²-5a+5)-1][(a²-5a+5)+1]-3=(a²-5a+5)²-1-3=(a²-5a+5+2)(a²-5a+5-2)=(a²-5a+7)(a²-5a+3).


(a-1)(a-2)(a-3)(a-4)-3=[(a-1)(a-4)][(a-2)(a-3)]
=[(a^2-5a)+4][(a^2-5a)+6]-3=(a^2-5a)^2+10(a^2-5a)+24-3
=(a^2-5a)^2+10(a^2-5a)++21=(a^2-5a+3)(a^2-5a+7)