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\(2x^3-3x^2+3x-1\)
\(=2x^3-x^2-2x^2+x+2x-1\)
\(=x^2\left(2x-1\right)-x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x^2-x+1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(5x^2-10x+2x-4\)
\(=5x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(5x+2\right)\)
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Lời giải:
$2x^2+3x-5=(2x^2-2x)+(5x-5)=2x(x-1)+5(x-1)=(x-1)(2x+5)$
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\(=2\left(x^2-y^2\right)-3\left(x+y\right)=2\left(x-y\right)\left(x+y\right)-3\left(x+y\right)=\left(x+y\right)\left(2x-2y-3\right)\)
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a) \(2x^2+5x+2\)
\(=2x^2+4x+x+2\)
\(=2x\left(x+2\right)+\left(x+2\right)\)
\(=\left(x+2\right)\left(2x+1\right)\)
b) \(4x^2-4x-9y^2+12y-3\)
\(=\left(4x^2-4x+1\right)-\left(9y^2-12y+4\right)\)
\(=\left(2x-1\right)^2-\left(3y-2\right)^2\)
\(=\left(2x-1+3y-2\right)\left(2x-1-3y+2\right)\)
\(=\left(2x+3y-3\right)\left(2x-3y+1\right)\)
c) \(x^4-2x^3-4x^2+4x-3\)
\(=x^4+x^3-x^2+x-3x^2-3x+3x-3\)
\(=\left(x^4+x^3-x^2+x\right)-\left(3x^2+3x-3x+3\right)\)
\(=x\left(x^3+x^2-x+1\right)-3\left(x^3+x^2-x+1\right)\)
\(=\left(x^3+x^2-x+1\right)\left(x-3\right)\)
d) \(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x^3-2xy^2-8x^2+8xy=2x\left(x^2-y^2\right)-8x\left(x-y\right)=2x\left(x-y\right)\left(x+y\right)-8x\left(x-y\right)=2x\left(x-y\right)\left(x+y-4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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`2x^3-3x^2+2x-1`
`=2x^3-2x^2-x^2+x+x-1`
`=2x^2(x-1)-x(x-1)+x-1`
`=(x-1)(2x^2-x+1)`
![](https://rs.olm.vn/images/avt/0.png?1311)