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(x+2)(x+3)(x+4)(x+5)-24
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ZT
1
VN
19 tháng 9 2017
Nhớ mình nha mình âm diểm rồi:
M=(x+2)(x+3)(x+4)(x+5)-24
M=(x2+3x+2x+6)(x2+5x+4x+20)-24
M=(x2+5x+6)(x2+9x+20)-24
M=x4+9x3+20x2+5x3 +14x+100x+6x2+54x+120-24
M=x4+14x3+26x2+168x+96
2 tháng 10 2021
\(x^2\left(x-3\right)^2-\left(x-3\right)^2-x^2+1=\left(x-3\right)^2\left(x^2-1\right)-\left(x^2-1\right)=\left(x^2-1\right)\left(x-3\right)^2=\left(x-1\right)\left(x+1\right)\left(x-3\right)^2\)
T
3
19 tháng 9 2017
\(M=\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+3\right)\left(x+4\right)\left(x+2\right)\left(x+5\right)-24\)
\(=\left(x^2+7x+12\right)\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)+1-25\)
\(=\left(x^2+7x+11\right)^2-25\)
\(=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+6\right)\)
12 tháng 11 2018
(x+2).(x+3).(x+4).(x+5)−24
=(x2+7x+10).(x2+7x+12)−24
=(x2+7x+10).(x2+7x+10+2)−24
Đặt x2+7x+10=t, ta có
t.(t+2)−24
=t2+2t−24
=t2+2t+1−25
=(t−1)2−25
=(t−1−5)(t−1+5)
=(t−6)(t+4)
=(x2+7x+10−6)(x2+7x+10+4)
(x2+7x+4)(x2+7x+14)
P/s tham khảo nha
8 tháng 11 2018
\(\left(x+2\right).\left(x+3\right).\left(x+4\right).\left(x+5\right)-24\)
\(\Leftrightarrow\left(x^2+7x+10\right).\left(x^2+7x+12\right)-24\)
\(\Leftrightarrow\left(x^2+7x+10\right).\left(x^2+7x+10+2\right)-24\)
Đặt \(x^2+7x+10=t\), ta có
\(t.\left(t+2\right)-24\)
\(\Leftrightarrow t^2+2t-24\)
\(\Leftrightarrow t^2+2t+1-25\)
\(\Leftrightarrow\left(t-1\right)^2-25\)
\(\Leftrightarrow\left(t-1-5\right)\left(t-1+5\right)\)
\(\Leftrightarrow\left(t-6\right)\left(t+4\right)\)
\(\Rightarrow\left(x^2+7x+10-6\right)\left(x^2+7x+10+4\right)\)
\(\Leftrightarrow\left(x^2+7x+4\right)\left(x^2+7x+14\right)\)
P/s tham khảo nha
1 tháng 9 2021
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-8=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\)
Đặt \(x^2+7x=t\)
\(\left(t+10\right)\left(t+12\right)-8=t^2+22t+120-8\)
\(=t^2+22t+112=\left(t+8\right)\left(t+14\right)\)
Theo cách đặt \(=\left(x^2+7x+8\right)\left(x^2+7x+14\right)\)
N
3
25 tháng 10 2021
\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\\ =\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\\ =\left(x^2+7x+11\right)^2-1-24\\ =\left(x^2+7x+11\right)^2-25\\ =\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\\ =\left(x^2+7x+6\right)\left(x^2+7x+16\right)\\ =\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
\(=\left(\left(x+2\right)\left(x+5\right)\right)\left(\left(x+3\right)\left(x+4\right)\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt \(x^2+7x+10=y\)ta có:
\(y\left(y+2\right)-24\)
\(=y^2+2y-24\)
\(=y^2-4y+6y-24\)
\(=y\left(y-4\right)+6\left(y-4\right)\)
\(=\left(y-4\right)\left(y+6\right)\)
\(=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x^2+x+6x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x\left(x+1\right)+6\left(x+1\right)\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)