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

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1. 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)

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2. `(x+2)(x+3)(x+4)(x+5)-24`

   `=[(x+2)(x+5)][(x+2)(x+3)]`

   `=(x^2+7x+10)(x^2+7x+12)-24`

   `=(x^2+7x+11-1)(x^2+7x+12+1)-24`

   `=(x^2+7x+11)^2-1-24`

   `=(x^2+7x+11)-5^2`

   `=(x^2+7x+11-5)(x^2+7x+11-5)`

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

    

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