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HN
1
0N
1
24 tháng 7 2018
\(x^4-4x^3+8x^2-16x+16 \)
\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3-2x^2+4x-8\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\)
\(=\left(x-2\right)^2\left(x^2+4\right)\)
BN
1
10 tháng 10 2017
\(x^{14}+16\)
\(=x^{14}+4^2\)
\(=x^{14}+8x^7+4^2-8x^7\)
\(=\left(x^7+4\right)^2-\sqrt{8x^7}^2\)
\(=\left(x^7+4-\sqrt{8x^7}\right)\left(x^7+4+\sqrt{8x^7}\right)\)
NN
3
KN
10 tháng 10 2019
\(x^{16}+4\)
\(=x^{16}-2x^{12}+2x^{12}+2x^8+2x^8-4x^8+4x^4-4x^4+4\)
\(=\left(x^{16}-2x^{12}+2x^8\right)+\left(2x^{12}-4x^8+4x^4\right)\)
\(+\left(2x^8-4x^4+4\right)\)
\(=x^8\left(x^8-2x^4+2\right)+2x^4\left(x^8-2x^4+2\right)\)
\(+2\left(x^8-2x^4+2\right)\)
\(=\left(x^8+2x^4+2\right)\left(x^8-2x^4+2\right)\)
10 tháng 10 2019
ミ★长 - ƔξŦ★彡: Làm dài vại:(
\(x^{16}+4\)
\(=\left(x^{16}+4x^8+4\right)-4x^8\)
\(=\left(x^8+2\right)^2-\left(2x^4\right)^2\)
\(=\left(x^8+2-2x^4\right)\left(x^8+2+2x^4\right)\)
TN
8
2 tháng 8 2016
\(x^4+x^3+x^2-1\)
\(=x^3\left(x+1\right)+\left(x+1\right)\left(x-1\right)\)
\(=\left(x+1\right)\left(x^3+\left(x-1\right)\right)\)
Ủng hộ nha ^ _ ^
AL
2 tháng 8 2016
\(x^4+x^3+x^2-1\)
\(=x^2\left(x^2-1\right)+x^2-1\)
\(=\left(x^2+1\right)\left(x^2-1\right)\)
KN
3 tháng 7 2019
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
KN
3 tháng 7 2019
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
LV
1
25 tháng 10 2017
Ta có : \(x^4+x^3+2x^2+x+1\)
\(=x^4+x^3+x^2+x^2+x+1\)
\(=x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2+1\right)\)
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 :
\(\left(x^2-10x+20\right)^2\)
\(=\left(x^2-2.5.x+25-25+20\right)^2\)
\(=\left[\left(x-5\right)^2-5\right]^2\)
\(=\left(x-5-\sqrt{5}\right)^2\left(x-5+\sqrt{5}\right)^2\)
Đặt \(A=\left(x+3\right)^4+\left(x+1\right)^4-16\)
\(=\left\lbrack\left(x+2\right)+1\right\rbrack^4+\left\lbrack\left(x+2\right)-1\right\rbrack^4-16\)
Đặt b=x+2
=>\(A=\left(b+1\right)^4+\left(b-1\right)^4-16\)
\(=\left(b^2+2b+1\right)^2+\left(b^2-2b+1\right)^2-16\)
\(=\left(b^2+1\right)^2+4b\left(b^2+1\right)+4b^2+\left(b^2+1\right)^2-4b\left(b^2+1\right)+4b^2-16\)
\(=2\left(b^2+1\right)^2+8b^2-16\)
\(=2\left\lbrack\left(b^2+1\right)^2+4b^2-8\right\rbrack\)
\(=2\left\lbrack b^4+2b^2+1+4b^2-8\right\rbrack=2\left(b^4+6b^2-7\right)\)
\(=2\left(b^2+7\right)\left(b^2-1\right)=2\left(b^2+7\right)\left(b-1\right)\left(b+1\right)\)
\(=2\left\lbrack\left(x+2\right)^2+7\right\rbrack\left(x+2-1\right)\left(x+2+1\right)=2\left(x+1\right)\left(x+3\right)\left\lbrack\left(x+2\right)^2+7\right\rbrack\)
Đặt \(A=\left(x+3\right)^4+\left(x+1\right)^4-16\)
\(=\left\lbrack\left(x+2\right)+1\right\rbrack^4+\left\lbrack\left(x+2\right)-1\right\rbrack^4-16\)
Đặt b=x+2
=>\(A=\left(b+1\right)^4+\left(b-1\right)^4-16\)
\(=\left(b^2+2b+1\right)^2+\left(b^2-2b+1\right)^2-16\)
\(=\left(b^2+1\right)^2+4b\left(b^2+1\right)+4b^2+\left(b^2+1\right)^2-4b\left(b^2+1\right)+4b^2-16\)
\(=2\left(b^2+1\right)^2+8b^2-16\)
\(=2\left\lbrack\left(b^2+1\right)^2+4b^2-8\right\rbrack\)
\(=2\left\lbrack b^4+2b^2+1+4b^2-8\right\rbrack=2\left(b^4+6b^2-7\right)\)
\(=2\left(b^2+7\right)\left(b^2-1\right)=2\left(b^2+7\right)\left(b-1\right)\left(b+1\right)\)
\(=2\left\lbrack\left(x+2\right)^2+7\right\rbrack\left(x+2-1\right)\left(x+2+1\right)=2\left(x+1\right)\left(x+3\right)\left\lbrack\left(x+2\right)^2+7\right\rbrack\)