Question

问一道数学因式分解……

（a+1)(a+3)(a+5)(a+7)+15的因式分解。

Answer 1

(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)(a²+8a+10)
=(a+2)(a+6)(a²+8a+10)

Answer 2

（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。

Answer 3

（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)

Answer 4

（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)

Answer 5

（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)