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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(x^2+3x-18\)
\(\Leftrightarrow x^2-3x+6x-18\)
\(\Leftrightarrow\left(x^2-3x\right)+\left(6x-18\right)\)
\(\Leftrightarrow x\left(x-3\right)+6\left(x-3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x+6\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=x^2-4x-5x+20\)
\(=x\left(x-4\right)-5\left(x-4\right)\)
\(=\left(x-4\right)\left(x-5\right)\)
x2 - 9x + 20
= x2 - 4x - 5x + 20
= x( x - 4 ) - 5( x - 4 )
= ( x - 4 )( x - 5 )
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=x^3+2x^2-8x=x\left(x^2+2x-8\right)\\ =x\left(x^2-2x+4x-8\right)\\ =x\left(x-2\right)\left(x+4\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(9x^3y^2+3x^2y^2\)
\(=3x^2y^2\cdot3x+3x^2y^2\cdot1\)
\(=3x^2y^2\left(3x+1\right)\)
b: \(x^2-2x+1-y^2\)
\(=\left(x^2-2x+1\right)-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1-y\right)\left(x-1+y\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
c: \(x^4+x^3-4x^2+x+1\)
\(=x^4-x^3+2x^3-2x^2-2x^2+2x-x+1\)
\(=\left(x-1\right)\left(x^3+2x^2-2x-1\right)\)
\(=\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+2x\left(x-1\right)\right]\)
\(=\left(x-1\right)^2\cdot\left(x^2+3x+1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x+1\right)^4+\left(x^2+x+1\right)^2\)
\(=2x^4+6x^3+9x^2+6x+2\)(bạn nhân phá ngoặc rồi thu gọn nhé)
\(=\left(2x^4+2x^3+x^2\right)+\left(4x^3+4x^2+2x\right)+\left(4x^2+4x+2\right)\)
\(=x^2\left(2x^2+2x+1\right)+2x\left(2x^2+2x+1\right)+2\left(2x^2+2x+1\right)\)
\(=\left(x^2+2x+2\right)\left(2x^2+2x+1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(3a\left(a-2b\right)+6b\left(2b-a\right)\)
\(=3a\left(a-2b\right)-6b\left(a-2b\right)\)
\(=3\left(a-2b\right)\left(a-2b\right)\)
\(=3\left(a-2b\right)^2\)
3a(a-2b)+6b(2b-a)
=3a(a-2b)-6b(a-2b
=(a-2b)(3a-6b)
=3(a-2b)(a-3b)
\(4x^3-13x^2+9x-18\)
\(=4x^3-12x^2-x^2+3x+6x-18\)
\(=4x^2\left(x-3\right)-x\left(x-3\right)+6\left(x-3\right)\)
\(=\left(x-3\right)\left(4x^2-x+6\right)\)