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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : x 3 - 6 x 2 y + 12 x y 2 - 8 y 3 = ( x ) 3 - 3 . x 2 . 2 y + 3 . x . ( 2 y ) 2 - ( 2 y ) 3 = ( x - 2 y ) 3
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : x 3 - 6 x 2 y + 12 x y 2 - 8 y 3 = ( x ) 3 - 3 . x 2 . 2 y + 3 . x . ( 2 y ) 2 - ( 2 y ) 3 = ( x - 2 y ) 3
![](https://rs.olm.vn/images/avt/0.png?1311)
x 3 – 6 x 2 y + 12 x y 2 – 8 y 3 = x 3 – 3 . x 2 . ( 2 y ) + 3 . x . ( 2 y ) 2 – ( 2 y ) 3 = ( x – 2 y ) 3
đáp án cần chọn là: D
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,x^3+6x^2y+12xy^2+8y^3\\ =x^3+3.2x^2+3.2^2.x+\left(2y\right)^3\\ =\left(x+2y\right)^3\)
\(b,x^3-3x^2+3x-1\\ =x^3-3x^2.1+3x.1^2-1^3\\ =\left(x-1\right)^3\)
a) \(x^3+6x^2y+12xy^2+8y^3\)
\(=x^3+3\cdot x^2\cdot2y+2\cdot x\cdot\left(2y\right)^2+\left(2y\right)^3\)
\(=\left(x+2y\right)^3\)
b) \(x^3-3x^2+3x-1\)
\(=x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3\)
\(=\left(x-1\right)^3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(l,=5x\left(y^2-2yz+5z\right)\\ m,=\left(x+1\right)^3-27y^3\\ =\left(x+1-3y\right)\left(x^2+2x+1+3xy+3y+9y^2\right)\\ n,=\left(x-3y\right)^2\\ o,=\left(x+2y\right)^3\\ p,=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\\ q,=\left(x+2y\right)^2-2\left(x-2y\right)+1\\ =\left(x+2y-1\right)^2\)
Ta có \(\left(x-2y\right)^3=x^3-6x^2y+12xy^2-8y^3=-8\)
\(\Rightarrow x-2y=-2\)
Do đó \(3x^2-12xy+12y^2=3\left(x^2-4xy+4y^2\right)=3\left(x-2y\right)^2\)
\(=3.\left(-2\right)^2=12\)