A=( 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
Đặt y=a2+8a+7 ta được :
y(y+8)+15=y2 + 8y +15
=y2 +3y+5y+15
=y(y+3) +5(y+3)
=(y+3)(y+5)
thay y=a2+8a+7 ta được
(a2+8a+7+3)(a2+8a+7+5)
=(a2+8a+10)(a2-2a-6a+12)
=(a2+8a+10)[a(a-2)-6(a-2)]
=(a2+8a+10)(a-2)(a-6)