PT
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Khách
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2 tháng 8 2016
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+16\)
\(=\left(x^2+8x+2x+16\right)\left(x^2+6x+4x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10+16+8\right)+16\)
\(=\left(x^2+10x+16\right)^2+2.\left(x^2+10x+16\right).4+4^2\)
\(=\left(x^2+10x+16+4\right)^2\)
\(=\left(x^2+10+20\right)^2\)
2 tháng 8 2016
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]+16\)
\(=\left(x^2+8x+2x+16\right)
\left(x^2+6x+4x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\left(1\right)\)
\(\text{Đặt }x^2+10x+\frac{16+24}{2}=t\)
\(\text{hay }x^2+10x+20=t\)
\(\left(1\right)\Rightarrow\left(t-4\right)\left(t+4\right)+16\)
\(=t^2-4^2+16\)
\(=t^2-16+16\)
\(=t^2\)
\(=\left(x^2+10x+20\right)^2\)
24 tháng 9 2019
\(\left(x-2\right)\left(x-4\right)\left(x-6\right)\left(x-8\right)+16\)
\(=\left[\left(x-2\right)\left(x-8\right)\right]\left[\left(x-4\right)\left(x-6\right)\right]+16\)
\(=\left(x^2-10x+16\right)\left(x^2-10x+24\right)+16\)(1)
Đặt \(x^2-10x+20=t\)thay vào (1) ta được :
\(\left(t-4\right)\left(t+4\right)+16\)
\(=t^2-16+16\)
\(=t^2\)Thay \(t=x^2-10x+20\)ta được :
\(\left(x^2-10x+20\right)^2\)
\(=\left(x^2-2.5.x+25-25+20\right)^2\)
\(=\left[\left(x-5\right)^2-5\right]^2\)
\(=\left(x-5-\sqrt{5}\right)^2\left(x-5+\sqrt{5}\right)^2\)
7 tháng 10 2018
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]+18\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(=\left(x^2+10x+20-4\right)\left(x^2+10x+20+4\right)-16\)
\(=\left(x^2+10x+20\right)^2-16+16=\left(x^2+10x+20\right)^2\)
Chúc bạn học tốt.
23 tháng 10 2019
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(\Rightarrow\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+6\right)\left(x+8\right)\right]+16\)
\(\Rightarrow\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(\Rightarrow\left(x^2+10x+16\right)\left[\left(x^2+10x+16\right)+8\right]+16\)
\(\Rightarrow\left(x^2+10x+16\right)^2+8\left(x^2+10x+16\right)+4^2\)
\(\Rightarrow\left(x^2+10x+20\right)^2\)
U
1
11 tháng 12 2015
\(=\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left(x+6\right)\left(x+4\right)\left(x+2\right)\left(x+8\right)+16\)
\(=\left(x^2+10x+24\right)\left(x^2+10x+16\right)+16\)
\(=\left(t+8\right)t+16=\left(t+4\right)^2=\left(x^2+10x+20\right)^2\)
TH
4
7 tháng 8 2016
x3 - x2 + 16x - 16 = x2(x - 1) + 16(x - 1) = (x2 + 16)(x - 1)
7 tháng 8 2016
x^3-x^2+16x-16 = (x^3-x^2)+(16x-16) = x^2.(x-1) + 16.(x-1) = (x-1)(x^2+16)
BC
2
27 tháng 10 2018
\(x^3+5x^2+3x-9\)
\(=x^3-x^2+6x^2-6x+9x-9\)
\(=x^2\left(x-1\right)+6x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)
\(x^{16}+x^8-2\)
\(=\left(x^{16}-1\right)+\left(x^8-1\right)\)
\(=\left(x^8-1\right)\left(x^8+1\right)+\left(x^8-1\right)\)
\(=\left(x^8-1\right)\left(x^8+2\right)\)
\(=\left(x^4-1\right)\left(x^4+1\right)\left(x^8+2\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+2\right)\)
H
27 tháng 10 2018
\(c,x^3+5x^2+3x-9\)
\(=x^3+6x^2+9-x^2-6x-9\)
\(=x\left(x^2+6x^2+9\right)-\left(x^2+6x^2+9\right)\)
\(=x.\left(x+3\right)^2-\left(x+3\right)^2\)
\(=\left(x+3\right)^2\left(x-1\right)\)
\(d,x^{16}+x^8-2\)
\(=\left(x^8+2x^4+1\right)-x^4\)
\(=\left(x^4+1\right)^2-x^4\)
\(=\left(x^4+1+x^4\right)\left(x^4+1-x^4\right)\)
HN
1
18 tháng 8 2017
\(x^3+9x^2+6x-16\)
\(=x^3+x^2-2x+8x^2+8x-16\)
\(=x\left(x^2+x-2\right)+8\left(x^2+x-2\right)\)
\(=\left(x^2+x-2\right)\left(x+8\right)\)
\(=\left(x^2-x+2x-2\right)\left(x+8\right)\)
\(=\left[x\left(x-1\right)+2\left(x-1\right)\right]\left(x+8\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x+8\right)\)
HK
1
28 tháng 8 2017
Ta có
(x2-3)2+16
=x4-6x2+9+16
=x4-6x2+25
=x4+10x2+25-16x2
=(x2+5)2-16x2
=(x2+5-4x)(x2+5+4x)
HN
1
NN
13 tháng 10 2020
\(x^3-9x^2+6x+16=\left(x^3+x^2\right)-\left(10x^2+10x\right)+\left(16x+16\right)\)
\(=x^2.\left(x+1\right)-10x\left(x+1\right)+16\left(x+1\right)\)
\(=\left(x+1\right).\left(x^2-10x+16\right)\)
\(=\left(x+1\right).\left[\left(x^2-8x\right)-\left(2x-16\right)\right]\)
\(=\left(x+1\right)\left[x\left(x-8\right)-2\left(x-8\right)\right]\)
\(=\left(x+1\right)\left(x-2\right)\left(x-8\right)\)
\(x^{16}+x^8-2=\left(x^{16}-1\right)+\left(x^8-1\right)\)
\(=\left(x^8+1\right)\left(x^8-1\right)+\left(x^8-1\right)\)
\(=\left(x^8-1\right)\left(x^8+1+1\right)\)
\(=\left(x^8-1\right)\left(x^8+2\right)\)
\(=\left(x^8+2\right)\left(x^4+1\right)\left(x^4-1\right)\)
\(=\left(x^8+2\right)\left(x^4+1\right)\left(x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^8+2\right)\left(x^4+1\right)\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\)