Đáp án:
`1.` `a-b=-10`
`2.` `a+b=-14`
Giải thích các bước giải:
Câu `1` :
`(x+2)(x+3)(x+4)(x+5)-24`
`=(x+2)(x+5)(x+3)(x+4)-24`
`=(x^2+7x+10)(x^2+7x+12)-24`
Đặt `x^2+7x+10=t`
`=t(t+2)-24=t^2+2t-24`
`=(t^2+2t+1)-25`
`=(t+1)^2-5^2=(t+1-5)(t+1+5)`
`=(t-4)(t+6)=(x^2+7x+10-4)(x^2+7x+10+6)`
`=(x^2+7x+6)(x^2+7x+16)`
Mà `(x+2)(x+3)(x+4)(x+5)-24=(x^2+7x+a)(x^2+7x+b)`
`->a=6,b=16`
`->a-b=6-16=-10`
Câu `2` :
`(x-1)(x-2)(x+4)(x+5)-27`
`=(x-1)(x+4)(x-2)(x+5)-27`
`=(x^2+3x-4)(x^2+3x-10)-27`
Đặt `x^2+3x-4=t`
`=t(t-6)-27`
`=t^2-6t-27=(t^2-6t+9)-36`
`=(t-3)^2-36=(t-3)^2-6^2`
`=(t-3-6)(t-3+6)=(t-9)(t+3)`
`=(x^2+3x-4-9)(x^2+3x-4+3)`
`=(x^2+3x-13)(x^2+3x-1)`
Mà `(x-1)(x-2)(x+4)(x+5)-27=(x^2+3x+a)(x^2+3x+b)`
`=[x^2+3x+(-13)][x^2+3x+(-1)]`
`->a=-13,b=-1`
`->a+b=-13+(-1)=-14`.
