因式分解:(a+1)(a+3)(a+5)(a+7)+15 a(a-b+2)-6b(b+1)
问题描述：
因式分解:(a+1)(a+3)(a+5)(a+7)+15 a(a-b+2)-6b(b+1)
(a+1)(a+3)(a+5)(a+7)+15
a(a-b+2)-6b(b+1)
答
(a+1)(a+3)(a+5)(a+7)+15
=(a+1)(a+7)(a+3)(a+5)+15
=(a²+8a+7)(a²+8a+15)+15
设a²+8a+11=A
(a+1)(a+3)(a+5)(a+7)+15
=(A-4)(A+4)+15
=A²-16+15
=A²-1
=(A+1)(A-1)
=(a²+8a+12)(a²+8a+10)
=(a+2)(a+6)(a²+8a+10)
a(a-b+2)-6b(b+1)
=a^2-ab+2a-6b^2-6b
=a^2-ab-6b^2+2a-6b
=(a+2b)(a-3b)+2(a-3b)
=(a-3b)(a+2b+2)