( x+2) (x+3) (x+4) (x+5) -24 giúp mình vs ạk

Đáp án:

(x + 2)(x + 3)(x + 4)(x + 5) – 24 = (x + 1)(x + 6)(x^2 + 7x + 16) 

Giải thích các bước giải:

(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 + 11 = t

=> (t + 1)(t – 1) – 24  = t^2 – 1 – 24

= t^2 – 25

= t^2 – 5^2 = (t – 5)(t + 5)

= (x^2 + 7x + 11 – 5)(x^2 + 7x + 11 + 5)

= (x^2 + 7x + 6)(x^2 + 7x + 16)

= (x^2 + x + 6x + 6)(x^2 + 7x + 16)

= [x(x + 1) + 6(x + 1)](x^2 + 7x + 16)

= (x + 1)(x + 6)(x^2 + 7x + 16)