Ta có : \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(\left(x+1\right)\left(x+4\right)\right)\left(\left(x+2\right)\left(x+3\right)\right)-24\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

- Đặt \(x^2+5x+5=a\)

\(=\left(a-1\right)\left(a+1\right)-24=a^2-1-24=a^2-25\)

\(=\left(a-5\right)\left(a+5\right)\)

Ta có: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24-24\)

\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)\)

\(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)

\(=x\left(x+5\right)\left(x^2+5x+10\right)\)

= (x+1)(x+4)(x+2)(x+3)-24

= (x² +5x+4) (x² +5x+6)-24

  Đặt x² +5x+4 =a

=>(x² +5x+4)(x²+5x+6)-24

= a(a+2)-24 = a² +2a-24

= a² +6a-4a-24

= a(a+6) - 4(a+6) = (a-4)(a+6)

= (x² +5x+a-4)(x² +5x+4+6) = (x² +5x)(x² +5x+10)

=(x+1)(x+4)(x+2)(x+3) - 24

=(x^2+5x+4)(x^2+5x+6) - 24

=(x^2+5x+5-1)(x^2+5x+5+1) - 24 [hằng đẳng thức a^2-b^2 nha] 

=(x^2+5x+5)^2-1^2-24

=(x^2+5x+5)^2 - 25

=(x^2+5x+5)^2 - 5^2

=(x^2+5x+5-5)(x^2+5x+5+5)

=(x^2+5x)(x^2+5x+10

\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

Đặt \(x^2+5x+4=t\)

\(\Rightarrow\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24=t\left(t+2\right)-24\)

\(=t^2+2t+1-25\)

\(=\left(t+1\right)^2-5^2\)

\(=\left(t+1+5\right)\left(t+1-5\right)\)

\(=\left(t+6\right)\left(t-4\right)\)

\(=x\left(x+5\right)\left(x^2+5x+10\right)\)

Ta có : \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\)\(\left(x+4\right)-24\)

= \(\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\) (*)

. Đặt \(x^2+5x+4=t\) (1)

(*) <=> \(t\left(t+2\right)-24=t^2+2t-24=\left(t-4\right)\left(t+6\right)\) (2)

Thay (1) vào (2) ta suy ra : \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\) \(\left(x+4\right)-24=\)\(\left(x^2+5x+4-4\right)\left(x^2+5x+4+6\right)\) = \(\left(x^2+5x\right)\left(x^2+5x+10\right)\) = \(x\left(x+5\right)\left(x^2+5x+10\right)\)

\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left[\left(x+1\right)\left(x+4\right)\right].\left[\left(x+2\right)\left(x+3\right)\right]-24\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

\(=\left(x^2+5x+4\right)^2+2.\left(x^2+5x+4\right)+1-25\)

\(=\left(x^2+5x+4+1\right)^2-5^2\)

\(=\left(x^2+5x+5-5\right)\left(x^2+5x+5+5\right)\)

\(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)

\(=x\left(x+5\right)\left(x^2+5x+10\right)\)

Ta có 

<=>(x+1)(x+4)(x+2)(x+3)-24

<=>(X^2+5x4)(x^2+5x+6)-24

Đặt x^2+5x+5=x    (1)

Ta có 

<=>(x+1)(x-1)-24

<=>x^2-25

Thay 1 vào x  ta có

(x^2+5x+5)^2-5^2

<=>(x^2+10)(x^2+5x)(dpcm)

\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\\ =\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\\ =\left(x^2+7x+11\right)^2-1-24\\ =\left(x^2+7x+11\right)^2-25\\ =\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\\ =\left(x^2+7x+6\right)\left(x^2+7x+16\right)\\ =\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

\(=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)+1-25\)

\(=\left(x^2+7x+11\right)^2-25=\left(x^2+7x+11+5\right)\left(x^2+7x+11-5\right)\)

\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)

=[(x+2)(x+5)][(x+3)(x+4)]−24=(x2+7x+10)(x2+7x+12)−24=(x2+7x+11)2−1−24=(x2+7x+11)2−25=(x2+7x+11−5)(x2+7x+11+5)=(x2+7x+6)(x2+7x+16)=(x+1)(x+6)(x2+7x+16)

Ta có : \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

\(\left(x^2+5x+4\right)^2+2.\left(x^2+5x+4\right)+1-25\)

\(=\left(x^2+5x+5\right)-5^2\)

\(=x\left(x+5\right)\left(x^2+5x-10\right)\)

M=(x^2+5x+4)(x^2+5x+6)-24

Đặt x^2+5x+5 là a        (1)

Từ 2 đk trên=>M=(a-1)(a+1)-24

=>M=a^2 - 1-24

=a^2-25

=(a-5)(a+5) và (1)

=(x^2+5x+5-5)(x^2+5x+5+5)

=(x^2+5x)(x^2+5x+10)

Bạncóchắccđâylàtoánlớp1khônghả????? 

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\\ =\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\\ =\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

Đặt \(x^2+7x+11=y\)

\(\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\\ =\left(y+1\right)\left(y-1\right)-24\\ =y^2-1-24\\ =y^2-25\\ =\left(y-5\right)\left(y+5\right)\\ =\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\\ =\left(x^2+7x+6\right)\left(x^2+7x+16\right)\\ =\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\\ =\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\\ =\left(x^2+7x+11\right)^2-1-24\\ =\left(x^2+7x+11\right)^2-25\\ =\left(x^2+7x+16\right)\left(x^2+7x+6\right)\\ =\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

Đặt \(t=x^2+7x+10\) ta có:

\(=t\left(t+2\right)-24=t^2+2t-24\)

\(=t^2-4t+6t-24\)\(=t\left(t-4\right)+6\left(t-4\right)\)

\(=\left(t-4\right)\left(t+6\right)=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

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

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

Đặt x^2+7x+10=a

a(a+2)-24

=a^2+2a-24

=(a-4)(a+6)

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

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