Đặt A=(x+2)(x+3)(x+4)(x+5)-24
=[(x+2)(x+5)].[(x+3)(x+4)]-24
=(x²+7x+10).(x²+7x+12)-24
=(x²+7x+11-1).(x²+7x+11+1)-24
Đặt t=x²+7x+11
⇒A=(t-1)(t+1)-24
=t²-1-24
=t²-25
=(t-5)(t+5)(*)
Thay t=x²+7x+11 vào A,ta có:
A=(x²+7x+11-5)(x²+7x+11+5)
=(x²+7x+6)(x²+7x+16)
=(x²+x+6x+6)(x²+7x+16)
=[x(x+1)+6(x+1)](x²+7x+16)
=(x+1)(x+6)(x²+7x+16)