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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)
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)
\(l,=5x\left(y^2-2yz+5z\right)\\ m,=\left(x+1\right)^3-27y^3\\ =\left(x+1-3y\right)\left(x^2+2x+1+3xy+3y+9y^2\right)\\ n,=\left(x-3y\right)^2\\ o,=\left(x+2y\right)^3\\ p,=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\\ q,=\left(x+2y\right)^2-2\left(x-2y\right)+1\\ =\left(x+2y-1\right)^2\)
Áp dụng: \(\left(A-B\right)^3=A^3-3A^2B+3AB^2-B^3\)
\(8y^3-12xy^2+6x^2y-x^3\)
\(=\left(2y\right)^3-3\left(2y\right)^2.x+3.2y.x^2-x^3\)
\(=\left(2y-x\right)^3\)