问一道数学因式分解……（a+1)(a+3)(a+5)(a+7)+15的因式分解.

（a+1)(a+3)(a+5)(a+7)+15
=[(a+1)(a+7)][(a+3))(a+5)]+15
=(a^2+8x+7)(a^2+8x+15)+15
=(a^2+8x+7)^2+8(a^2+8x+7)+15
=(a^2+8x+7+3)(a^2+8x+7+5)
=(a^2+8x+10)(a^2+8x+12)
=(a+2)(a+6)(a^2+8x+10)

（a+1)(a+3)(a+5)(a+7)+15
=(a^2+7a+a+7)(a^2+5a+3a+15)+15
=(a^2+8a+7)(a^2+8a+7+8)+15
=(a^2+8a+7)^2+8(a^2+8a+7)+15
=(a^2+8a+7+3)(a^2+8a+7+5)
=(a^2+8a+10)(a^2+8a+12)
=(a^2+8a+10)(a+6)(a+2)
额。手好慢。上面三个级这么高的。

（a+1)(a+3)(a+5)(a+7)+15
=（a^2+8a+7)(a^2+8a+15)+15
=(a^2+8a)^2+22(a^2+8a)+120
=(a^2+8a+10)(a^2+8a+12)
=(a^2+8a+10)(a+2)(a+6)

（a+1)(a+3)(a+5)(a+7)+15
=（a+1)(a+7)(a+3)(a+5)+15
=（a^2+8a+7）(a^2+8a+15)+15
=(a^2+8a+7)^2 +8(a^2+8a+7)+15
=(a^2+8a+7+3)(a^2+8a+7+5)
=(a^2+8a+10)(a^2+8a+12)
=(a+2)(a+6)(a^2+8a+10)

(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)所以,原式=(a²+8a+12)(a&sup...