因式分解:(a^2+7a+12)(a^2-5a+6)-112
1个回答

=(a+3)(a+4)(a-2)(a-3)-112

=【(a+3)(a-2)】【(a+4)(a-3)】-112

=(a²+a-6)(a²+a-12)-112

=(a²+a)²-18(a²+a)+72-112

=(a²+a)²-18(a²+a)-40

=(a²+a)²-18(a²+a)+81-121

=(a²+a-9)²-11²

=(a²+a-9+11)(a²+a-9-11)

=(a²+a+2)(a²+a-20)

=(a²+a+2)(a+5)(a-4)